The 18-year-old was rushed to hospital after falling ill during the clash against Middlesbrough on Saturday.
But Clarke required emergency assistance towards the end of the game and received oxygen before being taken away on a stretcher.
Clarke was released from hospital on Teesside on Saturday evening and Angus Kinnear, the Leeds chief executive, said: "Jack spent the night under the supervision of the medical staff from the club and will return home today".
Straight after the game head coach Marcelo Bielsa said there had been concerns about Clarke's health, but he had recovered by the time he reached the dressing room after receiving treatment from paramedics.
Meanwhile, Middlesbrough boss Tony Pulis passed on his best wishes to Clarke when he addressed the media. "He was taken to hospital to see if he is alright".
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Obviously we're missing a couple of key players, but I don't know if it's the right time to change our ID. 'The players and the supporters have been looking forward to this, ' Solskjaer said .
"Jack has had messages from football fans from every club you can imagine and we all really appreciate it", he wrote.
Clarke has made 16 league appearances for Leeds this season, scoring two goals and attracting interest from Premier League clubs during the January transfer window.
They sit a point ahead of Norwich who face rivals Ipswich on Sunday, live on Sky Sports Main Event HD and Sky Sports Football HD.
They also extended their hold on an automatic promotion place over third-placed Sheffield United back to three points, matching the Blades' 3-3 draw with Aston Villa on Friday.