It was confirmed on Friday (December 16) that Spears had accepted her former agent's proposal, with Trawick saying that the couple were both "over the moon".
Federline responded to the announcement by congratulating his ex-wife, with whom he has two sons, saying that he is pleased to see her "in a good place".
"I'm really happy for her - I think he's a great guy," Glamour quotes him as saying. "She's happy; she's doing really well. I want to say she's in a good place.
"I haven't spoken to her much since I've been over here [in Australia], both of us have been busy with her being on tour, but I do know from talking to the kids and talking to the kids' teachers that they're doing really good."
Spears and Federline married in September 2004 and divorced two years later. Their children Sean Preston and Jayden James were born in 2005 and 2006 respectively.
She wed childhood friend Jason Allen Alexander in Las Vegas eight months before tying the knot with Federline. Their union was annulled after just 55 hours.
Spears and Trawick celebrated their engagement at his 40th birthday party in Vegas this weekend, which the popstar described as "one of the most magical nights of [her] life".
Watch Britney Spears in the video for 'Hold It Against Me' below: