In early 1980, Greene had a role on the daytime drama Together (Southern Television/ITV), which began in January. She first appeared on Blue Peter after appearing in the BBC adaptation of Pamela Brown's The Swish of the Curtain, following which she was asked by the programme's Editor Biddy Baxter to be the replacement for the outgoing Tina Heath. At the time Greene was the youngest ever presenter of Blue Peter, aged 22 and within two weeks was filming in Cornwall for the show. The programme won BAFTA during Greene's 3-year tenure. After leaving Blue Peter, she presented Saturday Superstore with Mike Read, and subsequently co-presented Going Live! with Phillip Schofield. It was during her time on Going Live! that Greene won "Best Female on TV" SOS Award 3 years running and famously presided over the phone-in where Five Star were asked "why are you so fucking crap?". She then began to appear in television commercials for Nescafé coffee. Later, she fronted Channel 4's daytime antiques programme Collectors' Lot.

On 10 September 1988 Greene and her partner Mike Smith, the television and radio presenter were seriously injured in a helicopter accident in Gloucestershire. The couple spent a number of weeks in hospital before Greene returned to present Going Live! while still in plaster.

In addition to presenting magazine shows such as the BBC's Pebble Mill and Good Morning Summer alongside Will Hanrahan, Greene has acted in the Doctor Who serial Attack of the Cybermen, Casualty, Brookside and French & Saunders. In 1992 she combined her talents in a hoax paranormal programme called Ghostwatch, alongside Smith and talk-show host Michael Parkinson. Greene and Smith made a foray into feature films in The Man Who Knew Too Little (1997), starring Bill Murray; they played presenters of The Theatre Of Life, a fictional English TV show which promised the participant a role in a crime drama.

In 1996 Greene began a four-year partnership with the Food Network, hosting a daily news, debate and magazine show. Later, Greene appeared in the ITV programme Have I Been Here Before? and was also a regular presenter on magazine show This Morning. She has also presented Discovery Home & Health's Weddings Live, an annual 6-hour broadcast which showcases several weddings live from across the country, from 2005 to 2007. Fellow presenters include Brendan Courtney and Celebrity makeup Artist and Stylist Armand Beasley. Partnered with Fred Palascak, Greene competed in the 2008 ITV Dancing on Ice competition.

Greene took part in an episode of BBC Wales's Coming Home programme, first shown on 22 December 2010. Her mother had died a month before filming but she decided to continue the process, alongside her 87-year-old father. The programme was able to trace her family tree back to the 17th century in Wales.

Greene became Ambassador for ovarian cancer charity Target Ovarian Cancer in 2012.

Greene and her husband, Mike Smith, appeared on Pointless on BBC One in December 2012. Mike Smith died on 1 August 2014 following complications after major heart surgery.

In April 2017, Greene guest presented an episode of This Morning alongside Phillip Schofield. She returned to guest present the show in July 2017, and again on 4 August 2017 and on 18 August 2017, alongside Rylan Clark-Neal.