The couple both shared a picture on social media on Sunday morning of her hand sporting a large ring.
Former baseball player Rodriguez wrote "she said yes", while Lopez simply posted several heart emojis.
Actress and pop star Lopez, 49, has been dating the retired sportsman, 43, since 2017.
She has had a number of previous high-profile romances and her ex-husbands include singer Marc Anthony, who she was married to for 10 years and with whom she had two children - twins Max and Emme.
Before that relationship she was married to choreographer Cris Judd and waiter and actor Ojani Noa, and she was also once engaged to Ben Affleck.
She had a five-year relationship with dancer Casper Smart, too.
Earlier this year, Lopez told Red magazine that she had to work out why she got into relationships that were not good for her before she could find happiness.
"I feel like I'm in my second, third, or fourth act," she said.
"I feel like I've lived several lifetimes already and I've had to figure myself out along the way, work out why I felt a certain way, or got into relationships that didn't serve me.
"And I finally realised: 'It's me. It's all me. I got to fix some stuff. I need to understand my own worth and value.'"
Discussing her relationship with Rodriguez, she added: "Both Alex and I are Latino. We are both self-made. He was always the hardest working baseball player that was - me, the same. We have that in common.
"We have the same work ethic. We also appreciate and know that coming from nothing, we always want to try to help and give back and teach our kids that."
According to US media reports, Rodriguez popped the question while the couple were on holiday in the Bahamas.
The photo shared by Lopez on Instagram attracted more than 2.6 million likes in just three hours.
© Sky News 2019