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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Gwent Police also confirmed the baby, discovered on wasteland close to Imperial Park on 29 January, was a boy.
The baby had been wrapped in a white towel with the words "St Annes" written along the edge and placed in the leather bag, police said.
The death is being treated as unexplained.
A post mortem previously showed the baby had been born at about full-term.
The force added it would be an "incredibly distressing" time for the baby's mother and it wanted to offer her "the right support".
Police have previously posted a video on social media urging the mother to get in touch.

The performer then forgot to switch his microphone off as he was sick.
Ramsey was only a few minutes from the end of his show at Aberdeen Music Hall when he felt sick.
The comedian, who was performing in the Granite City as part of a UK-wide tour, had earlier warned his audience that he was unwell.
He told fans on his twitter: "As a lot of you will already know, I had to run off stage last night in Aberdeen and projectile vomit was all over the place. It was beyond grim."
As well as stand-up, Ramsey starred as Jack Pearson in BBC Two sitcom Hebburn, set near his home town of South Shields in north east England.
Ramsey has also appeared on the BBC's Live at the Apollo and is a regular panellist on Channel 4 series Celebrity Juice.
Hearts have announced that their captain, Perry Kitchen, has moved to Danish Superliga club Randers.
[NEXT_CONCEPT]
Police searching for the mother of a newborn baby found dead in Newport have released an image of a bag identical to the one the child was found in.
[NEXT_CONCEPT]
Stand-up comedian Chris Ramsey has apologised to his audience in Aberdeen after running off stage during his show to vomit.