They issued a joint statement Monday, telling Page Six ... "We have made the difficult decision to divorce. As two people that love and care for one another very much, we politely ask for respect of our privacy at this time as we navigate this new phase of our lives."

The outlet reports they've been growing apart for quite some time and have recently been spending time apart to figure out a path forward.

The two actors got together in 2014, and were engaged 6 months later. They got married in 2015 --- but never had any children together ... although Sofia has a son from a previous relationship. They've often been considered one of Hollywood's big-time power couples.

Vergara -- whose been overseas celebrating her 51st birthday over the past several weeks -- appears to have been telegraphing she may be a single woman ... posting a ton of hot shots of herself in a bathing suit, with no sign of Joe in any of her recent snaps. Granted, the guy's been busy on the East Coast lately filming a new movie with Vince Vaughn ... pre-strike.

This is Sofia's second marriage and Joe's first. SV was in a long-term relationship with businessman Nick Loeb before she hooked up with Joe ... the remnants of which proved to be dramatic, as their embryo case dragged on for years in court.

Here's hoping this uncoupling isn't as eventful.