Amy Robach and T.J. Holmes Step Out Together in Miami

Amy Robach and T.J. Holmes are spending time together.

The GMA3 co-anchors visited a convenience store together in Miami on Dec. 27, with Robach, 49, smiling in matching grey sweats and flip-flops. Holmes, 45, looked low-key in dark grey Aviator Nation sweats, a white long-sleeved shirt and red baseball cap.

It comes after photos of the couple sharing a kiss surfaced on Dec. 30, a month to the day after their off-camera romance became widely known. In the photos, the couple walk along the beach in Miami, locking arms and taking in the boardwalk sights.

On Thursday a source told PEOPLE that the pair “are in love” and okay with putting their budding romance out in the open.

“They spent the holidays together and are spending all of their time together right now,” added the source. “They are fully in a relationship. They are not hiding anything at all because they have no reason to.”

The TV personalities first sparked dating rumors on Nov. 30 after photos surfaced of them holding hands in a car, during a vacation in upstate New York and cozying up at a bar in New York City. Hours after the photos surfaced, Holmes, 45, and Robach, 49, shut down their respective Instagram accounts (Robach has since reactivated her account while Holmes’ account remains inactive).

The pair have not publicly commented on their relationship, though they alluded to the news during a broadcast of GMA3: What You Need To Know in December. Holmes and Robach were taken off air on Dec. 5 and remain on hiatus as ABC investigates their relationship.

Both co-anchors wed their spouses in 2010; Robach married actor Andrew Shue while Holmes married attorney Marilee Fiebig.

According to public court records, Holmes and Fiebig filed for divorce after 12 years of marriage on Dec. 28. The source tells PEOPLE that Holmes “told some people he was unhappy in his marriage and had been for awhile” before filing for divorce. The pair share a daughter named Sabine.

The status of Robach’s marriage remains unclear, but a source previously told PEOPLE that she and Shue separated in August.

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The source added that the two began dating only after they each split from their respective spouses. “This was two consenting adults who were each separated. They both broke up with their spouses in August within weeks of each other,” the insider said. “The relationship didn’t start until after that.”

Another insider told PEOPLE, “Amy was going through a heartache and TJ was very much there for her and helpful, and that is when they started something.”