"We've decided to end our marriage," they say in a statement

“After long and careful consideration on both our parts, we’ve decided to end our marriage,” they say in a joint statement. “We entered our relationship with love and it’s with love and kindness we leave it. While privacy isn’t expected, it’s certainly appreciated.”

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According to a source, Johansson initiated the split. The actress has started apartment-hunting in New York City and is currently in Jamaica with some girlfriends, the source adds.

However, last month the pair were spotted looking cozy together at New York hotspot Avenue.

Johansson, 26, and Reynolds, 34, tied the knot in a quiet September 2008 ceremony in a wilderness retreat in Vancouver, which is Reynolds’s hometown. The ceremony was attended only by a handful of close family and friends – and no photos were released.

“It was my mission to have a moment of privacy, to do something for myself,” Johansson told the Los Angeles Times of the hush-hush affair. “I was happy with the results of that.”

The pair remained fairly mum about their relationship, only rarely giving up small tidbits about their married life.

But the actress told In Style in April 2010 that she enjoyed cooking for Reynolds – and her domestic life with him. “There’s a nice comfort in that. That part of your life is certain, in a way. You’ve got your home in that other person.”

Reynolds, who is PEOPLE’s Sexiest Man Alive, told PEOPLE that the best thing about married life was, “You get to hang out with your best buddy every day.”