A source tells PEOPLE that Lauren Sanchez and Jeff Bezos are "very much together, and will be moving in with each other"

Jeff Bezos and Lauren Sanchez are still going strong now that their relationship is public.

“They are very much together, and are planning to move in together,” a source tells PEOPLE.

News of the Amazon CEO’s romance with the news anchor and helicopter pilot, 49, first broke in early January after Bezos, 55, announced his divorce from wife MacKenzie after 25 years together in a joint statement on Twitter. Their split is likely to be one of the most expensive ever — since Bezos is the richest man in the world worth an estimated $137 billion.

While Sanchez and Bezos have not been spotted out together since news of their relationship broke, a source told PEOPLE in last week’s issue the new couple is “in constant contact.”

Sanchez was seen out in New York City on Tuesday enjoying dinner with a friend. “She looked like she was having a great time,” another source tells PEOPLE.

Last Friday, Bezos made his first public outing since he announced his divorce at the 16th Annual Living Legends of Aviation Awards hosted by John Travolta.

Credit: Todd Williamson/Getty

Bezos and Sanchez struck up a working relationship while collaborating on several projects together and “gradually” fell for each other, a source close to the couple said previously.

The source added that MacKenzie and Sanchez’s husband, Hollywood agent Patrick Whitesell, were aware of their relationship for a while before it became public.

“Their families dealt with this in the fall,” says the source. “The world is catching up to it, but it has had zero impact on their relationship. They’ve never been stronger.”

Bezos and MacKenzie have four children: three sons and a daughter. Sanchez is also divorcing her husband after 13 years of marriage, PEOPLE confirmed. They have two children together. She also has a son from a previous relationship.