He was born in Cambridgeshire, the son of Dilys (née Jackson) and David Vibert, both artists. He attended the Royal Academy of Dramatic Art from 1983 to 1986.
Vibert made his screen debut in 1989 in the TV series Traffik. He appeared in the BBC's The Buccaneers, in ITV's Cadfael, and in Van der Valk. He appeared in Jeeves and Wooster as Wilmot, Lord Pershore ('Motty'). In 1996, Vibert appeared at the National Theatre in Helen Edmundson's adaptation of Leo Tolstoy's War and Peace. He played Maximilien Robespierre in the BBC's adaptation of The Scarlet Pimpernel.
Vibert appeared in the Midsomer murders episode "Death in Chorus". He also appeared in the Waking The Dead episode "Subterraneans" and an episode of The Sarah Jane Adventures, "The Last Sontaran". In 2009 in Lewis he played the part of Simon Monkford a key role in Lewis' story arc as the man who had knocked down and killed Valerie Lewis in a hit and run some years earlier.
