"Alec proposed to Hilaria this weekend & we're all excited 4 the newly engaged couple," Matthew Hiltzik wrote on April 2. "AB's birthday's tom'w. Great way 2 celebrate!"
Baldwin first introduced Thomas to his fans during an appearance on the "Late Show" in August.
"I have a woman in my life, who's very important to me, my girlfriend," Baldwin told host David Letterman. When asked how long they'd been dating, the actor joked, "On a spiritual level, I've known her forever, Dave."
Over the summer, the "30 Rock" actor sold his Upper West Side apartment to move in with Thomas in SoHo. Thomas teaches yoga at the Union Square studio Yoga Vida and has had a healthy effect on Baldwin, who slimmed-down in recent months.
This will be the second marriage for Baldwin, whose nine year marriage to actress Kim Basinger ended in divorce in 2002. This will be Thomas' first marriage.
Baldwin has one daughter from his marriage to Basinger, 16-year-old Ireland who Tweeted on Monday, "Congratulations to @AlecBaldwin an @hilariathomas on getting engaged! Love you guys." She added later, "I'm going to be a flower girl."
Thomas responded to her future stepdaughter on Twitter, writing, "love you mas xoxo."
Thomas, who was born in Mallorca, Spain met Baldwin in early 2011 while dining with friends at Pure Food and Wine, a raw food restaurant in New York City. The couple has yet to set a date for the wedding.
In January, Baldwin opened up about the relationship on "Piers Morgan Tonight," telling the British host, "I got divorced, I dated people and I had one girlfriend for several years, and right before I met Hilaria, I did lay in my bed and say, 'This is it. I'm gonna be alone for the rest of my life, I'm gonna die alone in this apartment in this bed, I'll have my friends, I'll have Twitter, I'll have Words with Friends, I'll have my New Yorker subscription... I'll have my quiet, unhappy life and then right when I put it all on the shelf... I walked into a restaurant... and I met this woman who is probably one of the greatest people I've ever met in my life."
The 53-year-old actor has played Jack Donaghy on the NBC comedy series "30 Rock" since it debuted in 2006 and has one season left on his contract with NBC and has said he will leave at that point. Baldwin has not ruled out a political career but told Leno that he would rather "spend some of that '30 Rock' money traveling the world with my girlfriend."
Baldwin will next appear in the film adaptation of the Broadway hit, "Rock of Ages," which is set for release on June 15, 2012. The film is based on the hit Broadway musical, which features 1980s "hair metal" hits from bands like Journey, Bon Jovi, and Twisted Sister. It also stars Tom Cruise, Russell Brand and Julianne Hough.
Baldwin, who has appeared in films such as "Beetlejuice" and "It's Complicated," portrays Dennis Dupree, an ex-rocker who runs a club in Los Angeles' famed Sunset Strip rock district in the film.