The 38-year-old actor paid tribute to the late screen icon's commitment to fighting the disease in a short film which was released on Monday, reports Entertainment Tonight.
In the clip, the 'Saving Mr Banks' star credits Elizabeth - who founded the Elizabeth Taylor AIDS Foundation in 1991 - for her "fearless" contribution to the cause.
Since its establishment, the foundation - which aims to fund education, direct care and services to people living with AIDS - has donated more than $15 million to 650 organizations across the world.
He said: "(The project is) a bright light on Elizabeth's fearless and tireless commitment to fighting HIV/AIDS.
"It is an honor to be a part of it."
It isn't the first time Colin has spoken of his close relationship with Elizabeth, who died of congestive heart failure aged 79 in 2011.
In an interview with US talk show host Ellen Degeneres following her death, he admitted to having a "romantic relationship" with the late actress.
He said: "I got to have an audience with her, and that was the beginning of a year-and-a-half or two years of what was a really cool - which feels like in my head - the last kind of romantic relationship I've had, which was never consummated."