The 2009 X Factor finalist tweeted: "I can't believe he's finally asked me...". Her publicist later confirmed the news, reports the Daily Mail.
The I'm a Celebrity winner revealed that she is pregnant with her second child - and first with Barnham - in October.
Solomon had told Fabulous magazine that she didn't expect to get married in the near future.
She said: "I've got a boyfriend who's very anti-marriage so I don't think it's going to happen. I really want to get married, though. It's every girl's dream to have that big day, isn't it?"
Painter Barnham reportedly asked her to marry him during a horse and carriage ride in Central Park, New York.
> Stacey Solomon to release Iceland track as single