Leeves made her screen debut with a small role in 1983 on British comedy television show The Benny Hill Show, and appeared as a Dancer in Monty Python's The Meaning of Life. She moved to the United States, where she performed in small roles. From 1986 to 1988, she had her first leading role in the short-lived sitcom Throb, and then secured a recurring part in the television sitcom Murphy Brown. She received further recognition for roles in films such as Miracle on 34th Street (1994), James and the Giant Peach (1996), Music of the Heart (1999), and The Event (2003).

In 1993, Leeves joined the cast of the television series Frasier. She played the eccentric, forthright, and allegedly psychic Mancunian Daphne Moon. By the start of the eighth season, Leeves was pregnant, and the Writers incorporated her pregnancy into shows as weight gain due to her character's stress from her relationship with Niles (portrayed by David Hyde Pierce). By the conclusion of Frasier, Leeves had received a Primetime Emmy Award for Outstanding Supporting Actress in a Comedy Series nomination in 1998 and also a Golden Globe Award for Best Supporting Actress – Series, Miniseries or Television Film nomination in 1995 for her role and had become the highest-paid British Actress in Hollywood.

Leeves has been married to Marshall Coben, a CBS Paramount Television executive, since 21 December 1996. They have two children; her pregnancy with daughter Isabella Kathryn Coben (born 9 January 2001) was written into a Frasier plot as a weight-gaining Problem for her character. Frasier co-star Peri Gilpin was in the delivery room when Isabella was born, and is her godmother. Leeves is godmother of Gilpin's daughter Stella, and lives next door to Gilpin in Los Angeles, California. Leeves' son, Finn william Leeves Coben (born 19 December 2003) has David Hyde Pierce and John Mahoney as godfathers.

Leeves provides guest vocals in The Penguins of Madagascar as Lulu, a female chimp, with which Phil falls in love. With Peri Gilpin, Leeves also set up the production company Bristol Cities (cockney rhyming slang for 'titties'). Their last project was in 2007 a pilot for a US remake of the British sitcom The Vicar of Dibley, with Kirstie Alley in the title role.

In 2010, Leeves was a guest star in two episodes in ABC's Desperate Housewives as Lynette and Tom's therapist, Dr. Graham. From 2010 until 2015, she played the 40-something ex 'eyebrow Artist to the stars' Joy Scroggs in the TV Land comedy, Hot in Cleveland, with Valerie Bertinelli, Wendie Malick (also her co-star in the final season of Frasier), and Betty White. In 2011, she was nominated Screen Actors Guild Award for Outstanding Performance by an Ensemble in a Comedy Series along with the rest of the cast.

In January 2012, Leeves posed in an ad for the NOH8 Campaign, which supports the LGBT community.

She had a recurring role in the television series Murphy Brown which provided her first period of success, playing Audrey, the smart but awkward girlfriend of Producer Miles Silverberg (played by Grant Shaud). Leeves also appeared as the troublesome Marla the Virgin in four risqué episodes of Seinfeld: "The Virgin", "The Contest", "The Pilot", and "The Finale – Part 2". During this period, Leeves was cast as Holly for the pilot of the US version of the science-fiction comedy Red Dwarf. She also had a role as a lesbian avant-garde Dancer in the 1985 film To Live and Die in L.A.