Inside the Longacre Theater, where the couple tied the knot, the space was still decorated with props from La Cage aux Folles, as well as huge bouquets of pink and red flowers in gold urns.
During the emotional ceremony, performed by Terry Lavell who was Grammer's costar in the Broadway hit musical, attendants read poems that the bride and groom had written for one another. As the couple listened, they appeared to be holding back tears, according to one guest.
After Walsh's brother, Stuart, sang "Feels Like Home" by Randy Newman, Grammer, 55, and Walsh, 29, recited traditional vows.
"They looked very happy," a wedding guest told PEOPLE after the ceremony, "really, really happy."
In addition to Lavell, the couple was attended by Grammer's two eldest daughters, Spencer and Greer, Walsh's sister, Sophie, and friend Angela Copeland. The women wore matching black dresses and Christian Louboutin pumps.
The bride wore a silk sheath gown with beaded straps and bodice – a custom design by Peter Langner for Mark Ingram, according to Access Hollywood. Grammer's son Jude, joined Walsh's brothers as groomsmen, and the best man was friend Carl DeGersdorff.
A Night at The PlazaImmediately following the ceremony, a small group of guests went to the Plaza Hotel for a lavish dinner in the Grand Ballroom, which was decorated by celebrity event designer Ed Libby.
A few hours later, guests returned to find the Grand Ballroom transformed: The tables were replaced with regal, gold lounge furniture, cocktail tables, and a massive dance floor, flanked by a stage on one side and sleek bar on the other.
"It was gorgeous, very classy," said one wedding guest. "It wasn't too much and it wasn't too little. They definitely did it right."
After dinner, the newlyweds cut the 55-inch-tall carrot cake by Sylvia Weinstock and shared the story of how they met: He was flying to see La Cage in London, and she was one of the flight attendants.
"It was really, really sweet," a guest told PEOPLE. "Kelsey is very good with words. He's an actor, so he was very articulate and sweet. She was, too, and very genuine."
Throughout the night, guests grooved on the packed dance floor while deejay Jason Fioto from Generation Events played tunes such as, "I Wanna Dance with Somebody" and "Don't Stop Believin'," which a source described as "songs that everybody could sing along with and dance to."
The bride and groom spent the entire night at each other's sides, said a guest, who added, "They seemed so genuinely in love and happy. They were dancing with each other the whole time and seemed to be having a lot of fun together, really a part of the festivities."
As the evening wound down, guests were treated to passed desserts, including mini ice cream cones and little smoothies.
According to a source, the newlyweds slipped out quietly just before the celebration ended.
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