Alex Rodriguez 'Did Everything on His Own with the Ring,' Source Says of His Proposal to J.Lo

Alex Rodriguez went engagement ring shopping for Jennifer Lopez all by himself.

The former MLB player, 43, pulled off proposal so perfect that the Second Act star, 49, had no idea it was even coming as they enjoyed a romantic Bahamas getaway together.

“He did everything on his own with the ring. It was a complete surprise [to Jen],” a source tells PEOPLE of the mega-carat emerald-cut sparkler A-Rod gave to J.Lo when he got on one knee.

Multiple diamond experts told PEOPLE that at a first glance, the gem appears to be at least 15 carats and valued at upwards of $1 million.

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“Our team of gemologists and diamond PhD’s estimate the emerald-cut diamond is 20 carats and worth around $4.5 million,” Ajay Anand, CEO of Rare Carat, said. “This estimate is if the stone is D-Flawless [a very rare, colorless gem]. Since it’s A-Rod, it very well could be!”

Shane Co.’s vice president of merchandise Alicia Davis adds, “The emerald-cut ring is widely known as the most elegant and classic cut of diamond,” she says. “Jennifer’s is featured on a classic solitaire band which perfectly showcases its timeless, elongated cut.”

Lopez and Rodriguez announced they had gotten engaged on Saturday, sharing matching photos of Lopez wearing her stunning diamond engagement ringt as Rodriguez romantically holds her hand.

“She said yes,” Rodriguez wrote, while Lopez simply captioned the image with eight heart emojis.

Sources tell PEOPLE that Lopez has been overwhelmed with joy since Rodriguez popped the question.

“Jennifer is ecstatic and so are their families and friends. Very few people knew Alex planned on proposing. It was very much a surprise for Jennifer,” the source says. “It was just how Alex wanted it.”

Though they haven’t started planning their nuptials just yet, one thing is certain. All of the couple’s children will “definitely” play a huge role in their upcoming wedding.

“For them both, they are still all about their family with the four kids. Their initial strong attraction for each other would have quickly faded if they had not been able to come together as a family,” a source told PEOPLE.

“Their kids all accepted each other and got along from the beginning. It’s always tricky when you merge families, but Jennifer and Alex did a great job from the start. The kids are amazing together. And they have wanted Jennifer and Alex to get married for a long time. They will all definitely be a huge part of the wedding,” the source added.

Lopez and ex-husband Marc Anthony, 50, have 11-year-old twins Maximilian “Max” David and Emme Maribel, while Rodriguez and ex-wife Cynthia Scurtis, 46, share daughters Ella, 10, and Natasha, 14.

A source first confirmed Lopez and Rodriguez’s relationship to PEOPLE in March 2017, noting that they “have been dating for a few weeks. The baseball pro later confirmed their relationship status during an appearance on The View.