The pair officially celebrated their two-year anniversary on 4 February, and the former Seattle Mariner, Texas Ranger and New York Yankee shared a heartfelt message to his now-fiancée.
This is the fifth engagement for Lopez and will be A-Rod's second marriage.
The couple have been dating since 2017.
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The 49-year-old posted the exact same photo on her account with a string of heart emojis. They have been in a relationship for over two years.
Lopez has been married and divorced three times, including a high-profile split with singer Marc Anthony.
She also had a five-year relationship with dancer Casper Smart. "We are meant to be, and how much you mean to me can not be put into words", A-Rod wrote.
Rodriguez, the retired 22-year Major League Baseball veteran who won a World Series with the 2009 Yankees, posted the photo with the classic caption "she said yes".
Alex was married to Cynthia Scurtis and has two daughters with her.