The couple were married for 10 years, having marked their anniversary on Monday.
“After much thought and careful consideration, we have made the difficult decision to divorce,” the couple tells PEOPLE in a joint statement. “We go forward with love and friendship for one another and a commitment to co-parenting our children whose privacy we ask to be respected during this difficult time. This will be our only comment on this private, family matter. Thank you for understanding.”
Garner, 43, and Affleck, 42, intend to seek mediation, says a source close to the couple.
The two are parents to three kids: Violet, 9, Seraphina, 6, and Samuel, 3.
The couple often enjoyed family time together at home in Los Angeles where they were frequently spotted on carpool, coffee and after-school activity outings with their brood.
But their marriage was also the subject of scrutiny over the years.
In a 2014 interview with InStyle, Garner spoke of the couple’s “mindful” marriage, noting that their relationship was no longer in the “courtship” phase – but that she was fine with it.
“You can’t expect to be courted all the time, and I don’t want to court him right now – I don’t have the energy!
“But we’re definitely in a very mindful place where we’re making an effort to be together, do things at the same time, and be loving.”
Affleck often spoke of how much Garner helped stabilize his life after it had become tabloid fodder in the years following his 2004 split with Jennifer Lopez.
“My wife was definitely around then,” Affleck told Playboy in 2013. “Getting to know her, falling in love with her and being connected with her gave me a foundation to reach out and say, ‘Okay, I’m going to do Hollywoodland. I’m going to direct Gone Baby Gone,’ ” Affleck said. “Those were the steps forward I needed to put positive stuff on the board.”
Garner returned the praise, telling InStyle in 2013, “We both know we couldn’t do what we do without each other. He has been amazing at finding ways of telling me how much he appreciates what I do. Honestly, I would do anything for that man, because I know it’s not to be taken for granted.”
The two met as costars on the the set of their 2003 film Daredevil and started dating soon afterward.