The Rollerball star, 68, passed away at a hospital in Chicago, Illinois on 2 August (13) after suffering complications from leukaemia.
She was married to Cleese for almost a decade before their amicable divorce in 1990 and was the mother of the star's grown-up daughter, Camilla.
Cleese has now spoken of his sorrow following her death, insisting she will be greatly missed.
He says, "Barbara was a wonderfully kind person and a superbly talented artist. She will be dearly missed."
Trentham appeared in films such as The Possession of Joel Delaney (1972) with Shirley MACLaine, and 1976's Sky Riders (1976). She also featured on the cover of Vogue magazine during her time as a model, and dated actors including Jack Nicholson and Warren Beatty.
She met Cleese in 1980 at a Monty Python show in Los Angeles and they were married five months later.
Cleese is now on his fourth marriage.