Dean was born at St George's Hospital at Hyde Park Corner, London in 1959. She attended the Hurst Lodge School in Sunningdale England. She left the school winning the 'De Valois Prize' for Drama.

In 1977 Felicity played a significant guest role as Sara in the 2nd episode of the first season of The Professionals entitled 'The Female Factor' (by Brian Clemens) starring opposite Gordon Jackson, Martin Shaw and Lewis Collins. English Novelist Rebecca West, perhaps best known for her reports on the Nuremberg Trials, personally picked Dean to play Laura Bowen, the heroine of her novel The Birds Fall Down in a five-part BBC adaptation produced by Jonathan Powell in 1978. Critically acclaimed, this led to Dean going on to play many parts on television including Guinevere in The Legend of King Arthur for the BBC in 1978, Belinda Harlowe in The Far Pavilions opposite Ben Cross and Rupert Everett in 1984, and the Lynda La Plante series Trial & Retribution in 1999.

Dean has had an extensive stage career. In 1982 she auditioned for the Royal Shakespeare Company and originated the role of Annie in Good by C. P. Taylor. This production transferred to London's West End and then to Broadway. Douglas Watt from the Daily News said "the performance and mounting of the work are flawless... in an eventually moving piece of theatre one of its assets is the fine work by Felicity Dean as mistress Anne". Walter Kerr of The New York Times offered that "Felicity Dean is excellent in the role". While Jack Knoll of Newsweek said " The cast are excellent, notably Felicity Dean as the nubile student who becomes Halders mistress"

In 1985 Dean played Betsy in the Hugh Hudson film Revolution opposite Al Pacino and Donald Sutherland. She has continued to work with Pacino on his own personal projects.

In 1987 Dean played Cynthia Goodburn in The Whistle Blower, again opposite Michael Caine alongside Nigel Havers.

She has also appeared in many popular television programmes between 1990 and 2009, including Midsomer murders, Peak Practice, Casualty, New Tricks, Rosemary & Thyme, Die Kinder, Van Der Valk, The Inspector Alleyn Mysteries, Kavanagh QC, Wycliffe, Hetty Wainthropp Investigates, Lovejoy, Doctors, and Murder in Suburbia.

In 1994 Dean played Imogen in Wicked Old Men for Director Jude Kelly at the West Yorkshire Playhouse. Dean played Fanny Wilton in the Richard Eyre production of John Gabriel Borkman at The National Theatre in 1996 opposite Paul Scofield, Eileen Atkins and Vanessa Redgrave. Dean received excellent national critical acclaim for this role. John Gross of The Sunday Telegraph wrote " Felicity Dean is particularly impressive as Erhart's soignee friend Mrs Wilton". Benedict Nightingale of The Times wrote "formidably played by Felicity Dean" of her interpretation. The Spectator added "Felicity Dean also gives a powerful star turn as Fanny Wilton" and Jack Tinker of The Daily Mail "The entire production is on this high plateau of performance. Not least Felicity Dean's seductive Mrs Wilton,the exotic bird of paradise in the nest. For an actor to dominate a scene in such company is a personal triumph indeed..."

In 1998 Dean took the role of Masha in Three Sisters at Birmingham Rep under the direction of Bill Bryden, opposite Charles Dance. For this Dean was nominated for The Critics Guild Award for Best Actress Charles Spencer The Daily Telegraph wrote of her performance "Among a fine cast Felicity Dean is outstanding, playing Masha with the lazy grace of an indulged cat. To see this poised woman reduced to untrammelled desperation when her lover leaves is deeply upsetting..." Jeremy Kingston The Times also wrote, "Felicity Dean's fierce Masha subtly shows Desire clambering out of boredom into hysterical grief at the departure of Charles Dance's quietly charismatic Vershinin" while Michael Coveney of The Daily Mail praised her performance as being played "with a powerful cocktail of anger melancholy and listlessness"

Dean went on to play Mrs Clay in Persuasion, directed by Roger Michell. She appeared in The Last of the Blonde Bombshells with Judi Dench and Ian Holm, again written by Alan Plater (2000), as Dido in Stuart: A Life Backwards in 2007, and as Elaine in the series Talk to Me with Max Beesley in 2007.

In 2002 she also received high critical acclaim for her roles in The Coast of Utopia directed by Trevor Nunn again at the National Theatre. 2003 saw her again under the direction of Barry Kyle, this time at Shakespeare's Globe as Regan in King Lear. Charles Spencer of The Daily Telegraph noted that "Felicity Dean doesn't confine herself merely to capturing Regan's spite. She brings a great blast of sexuality to the stage,presenting a woman who is clearly turned on by evil.The effect is both thrilling and profoundly discomforting"

In 2007 she played the role of Dona Elvira in Don Juan, directed by Neil Bartlett at the Lyric Hammersmith. David Giles cast her in 2009 in Underfoot in Showbusiness, a fast-paced new comedy from acclaimed New York Writer Charles Leipart. Giles cast her again in 2009 as Pamela Harriman in another Charles Leipart play, Swimming at The Ritz, a two hander based around the life of Harriman in which Dean played opposite Jos Vantyler. After Giles' death in early 2010, the production was revived, due to its initial success, this time under the direction of Roland Jaquarello. It would see Dean again being awarded rave reviews for her role as Harriman and continuing to play into 2011.

In 2011 Dean played the role of Jacqui in The Wedding Video directed by Nigel Cole opposite Dame Harriet Walter, Rufus Hound and Robert Webb.

In September 2013 Sir Jonathan Miller directed the Gala Performance of william Shakespeare's King Lear at The Old Vic in London. Dean played Goneril opposite, Joss Ackland as King Lear, Michael York, Tony Robinson, Greta Scacchi, Honeysuckle Weeks, John Nettles, Robert Young, Tony Britton, Shaun Dooley, Barrie Rutter and Jos Vantyler.

In 2014 Dean played the lead role in The Long Road South alongside Michael Brandon, a new play by Paul Minx. The press said of Deans performance "Felicity Dean, playing the best drunk ma in her nightdress since Lindsay Duncan in That Face." "Felicity Dean's Carol Ann marks the play's standout performance as she quakes about the stage in sliver heels, brimming with morose longing.". "Dean who is the stand-out performer in this piece; her performance displaying scope, skill, and an admirable lack of Vanity.".

In 2017 she played the aged Queen Elizabeth I in the docu-drama Elizabeth I narrated by Drs Susannah Lipscombe and Dan Jones.