Meg Ryan and John Mellencamp Step Out in New York City After Announcing They're Engaged

Meg Ryan and John Mellencamp spent part of their Monday strolling the New York City streets together.

The newly engaged couple were spotted out for the first time since they broke the news last month, as they ran errands in the Big Apple.

Ryan, 57, wore a buttoned-up wool green trench coat with green pants and black sneakers. The actress, who kept her blonde locks down, carried a cross-strap bag and accessorized her look with gold sunglasses.

Mellencamp rocked a pair of matching sunglasses too. The singer, 67, was layered to battle the cold in a pair of overalls, which he paired with a white T-shirt, a black leather coat, and a pair of black kicks.

This will be the second marriage for Ryan who was wed to actor Dennis Quaid for 10 years (and shares a son, Jack, 26), and the fourth for Mellencamp, who has five kids from his three previous marriages.

The pair began dating in 2011 after Mellencamp ended his 18-year marriage to model Elaine Irwin, and were together for three years before calling it quits in August 2014. At the time of their split, a source told PEOPLE that “distance” had led to the relationship’s demise — with Ryan living in New York City with her daughter Daisy, 14 (whom she adopted in 2006), and Mellencamp preferring to stay in his home state of Indiana.

Though he moved on and dated Christie Brinkley for a year, there was hope of a reconciliation. “I loved Meg Ryan,” the “Jack and Diane” singer told Howard Stern in 2017. “She hates me to death. I think it’s because I’m a child. I throw fits, I gripe, I complain. I’m moody.”

By June 2017, Ryan and Mellencamp had rekindled their romance, a source then telling PEOPLE, “They have a bond.” Nearly a month ago, an excited Ryan shared the news on her engagement to Instagram. “ENGAGED!” she wrote on Nov. 8, next to a sweet and silly cartoon drawing of she and Mellencamp reaching for each other’s hands.

Throughout it all, Ryan and Mellencamp have kept their romance mostly private, with a rare public outing here and there — including a Christmas Day 2017 New York Knicks basketball game they caught with her son Jack and Mellencamp’s son Hud, 24, from his marriage to Irwin.

“John and Meg are a great combination,” a source close to the rocker told PEOPLE in November. Added an entertainment insider: “They relate on many levels. John loves her intellect, personality and sense of humor. Meg is in awe of his talent.”

When they venture out to a restaurant or to listen to music on Daufuskie Island in South Carolina, where the singer has a home, “they only have eyes for each other,” said the Mellencamp source.

Now with wedding plans likely underway, it remains to be seen where the couple will call home. “They have different lifestyles but they’re busy enough to be able to handle their differences,” added the entertainment source. “They are old enough to know what they want.”