The 25-year-old United States midfielder played 45 times for Hearts since joining them in March 2016 from DC United but at the tail end of last season found himself out of favour under head coach Ian Cathro.
He joins Randers on a two-year deal.
Of the side who finished seventh last season, Kitchen said: "It's a really good opportunity for me at this time."
New Hearts signing Ashley Smith-Brown limped off after only 27 minutes of his first outing for the Edinburgh side, a 1-0 friendly defeat by St Patrick's Athletic.
But Cathro said the on-loan Manchester City left-back, who had himself come on as a half-time substitute, was replaced with 21-year-old Angus Beith as a purely precautionary measure.
"He just felt something when he turned and this is a point in the season where you just don't need to take any risks," said the head coach.
"We'll just manage that and make sure it's okay.
"Pre-season is about building our conditioning and also about trying to avoid injury as best we can."
Fellow new signing Kyle Lafferty also made his first appearance in a Hearts shirt after being introduced with quarter of an hour left.
Cathro revealed he will treat the Northern Ireland striker, who has started just 22 club games in the last three seasons, cautiously as he looks to build up his fitness.
"It was important that Kyle got minutes," he said. "He's not had anywhere near as many training sessions as everyone else, so we're just going gradually with that.
"But it was good for him to get on to the pitch and we'll go step by step to build him up.
"We played against a team that's pretty much in the full flow of their season, so it's a really good match."
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Hearts have announced that their captain, Perry Kitchen, has moved to Danish Superliga club Randers.