Mendes, who won the Academy Award for best director for American Beauty, has been recognised for services to drama.
The director of two Bond films said he was “amazed, delighted and extremely proud” to receive the honour.
McQueen – recognised for services to art and film – is the first black film-maker to win the best picture Oscar, for 2013’s 12 Years a Slave.
Before moving into movies, both men enjoyed successful careers in other aspects of the arts.
Mendes, 54, built his early reputation on the stage, as artistic director of London’s Donmar Warehouse and for his productions of such musicals as Oliver! and Cabaret.
“I have stood on the shoulders of so many collaborators and colleagues over the last 30 years – actors, writers, designers, producers, technicians – to whom I owe a huge debt of gratitude,” he said.
“I would not be receiving this honour without them.”
McQueen won the Turner Prize in 1999 for his film and video works – fending off competition from the likes of Tracey Emin.
The 50-year-old is currently working on a TV series set within London’s West Indian community.
Reading-born Mendes began his career in the theatre, directing productions for the National Theatre, the Royal Shakespeare Company and the Donmar Warehouse.
He won a Laurence Olivier award in 1995 for directing The Glass Menagerie, and another the following year for his revival of the musical Company.
American Beauty, his first film, saw him win best director honours at the 2000 Golden Globes and the Oscars that followed.
His other films included Jarhead, Road to Perdition and 2008’s Revolutionary Road, which starred his then-wife Kate Winslet,
His other film credits include 2012’s Skyfall and 2015’s Spectre, the two recent instalments in the James Bond series.
His upcoming war epic, 1917, tells of two young British soldiers racing against time to avert an assault on their comrades.
In 2000 Mendes was made a CBE for services to drama.