Cowell and Silverman's family were holidaying together so their son Eric, 7, and Silverman's eldest son Adam were there to share the special occasion.
Reps for Cowell confirmed the engagement, and a source told People "they are both super happy.
"They've been together a long time now and adore each other so it's not a huge surprise to their close friends."
Another unnamed source told Page Six the proposal was "super sweet".
Silverman and Cowell met in 2004. Silverman was still married to her husband Andrew at the time, who was a good friend of the America's Got Talent judge.
Laura and Andrew Silverman finalised their divorce in 2013, and Cowell later admitted he had an affair with her while she was still married.
"[The affair] is not something I am proud of or wanted to happen in terms of hurting anyone," he said in 2013.
"It just happened … But then, of course, you have a baby, and you look at the baby and you kinda go, 'This is what happened from it.'"
At the time of the birth of his son Eric in 2014, Cowell gushed about being a father.
"I never knew how much love and pride I would feel," he wrote.
The engagement comes after Cowell's previous comments where he declared marriage wasn't something he was considering.
"I don't believe in marriage, not in this business," he has said.
The Daily Mail reports there have been rumours Silverman had an eye on an expensive engagement ring Cowell has had locked in a safe.
An insider shared with the news outlet: "He's never given the ring to her and never proposed. Getting married is an obsession of hers, that is her goal in the relationship - but he will not do it."
