The club called in finance troubleshooters on June 19 last year after mounting up debts of almost £30million.
But administrator Bryan Jackson of BDO confirmed the club had now been given the green light to resume normal operations.
He said: "I'm relieved. It has been a difficult year but now the club can move forward."
Hearts' very future was put in doubt last year as former owner Vladimir Romanov's Lithuanian business empire crumbled around him.
But a £2.5million rescue bid was put together by new chairwoman Ann Budge and fans' group the Foundation of Hearts which ultimately saved the club from being liquidated.
Budge has now taken charge of shares owned by Ukio Bankas and UBIG - Romanov's former companies which were also Hearts' major creditors and shareholders - but she will eventually cede control to the FoH.
The fans' group has 8,000 paying members who moved to secure the club's future when it was under serious threat.
For accountant Jackson, Hearts become the latest club to be thankful for his efforts.
He has already helped pull Clyde, Dundee, Dunfermline, Motherwell and Portsmouth from the brink and he said: "I've not got a bad record - I've not lost a club yet.
"You need a lot of luck and the support of the fans and in this latest case, that is exactly what we got.
"The club have got a lot of rebuilding to do but now they can move forward without things like a transfer embargo inhibiting them.
"It also means Ann and her team can get cracking without the likes of me being in their way."
Hearts' perilous financial state took a brutal toll on the club's football operations.
They were fined 15 points by the Scottish Professional Football League at the start of last season and banned from signing new players.
That left boss Gary Locke with an impossible task and his side were inevitably relegated from the top flight.
Budge's first act when she took effective control of the Tynecastle outfit last month was to axe Locke and promote Robbie Neilson from youth-team boss to become the club's new coach.
Former boss Craig Levein was also tempted back to Gorgie as he was named the club's director of football and, with the administration nightmare now officially over, they will once again be given the thumbs up to sign players.
Neilson has already been linked with moves for released Hamilton striker James Keatings and former Dundee United midfielder Morgaro Gomis.
But for the fans, they will finally be able to breath easily after 357 days of turmoil.
In a tweet, the Foundation of Hearts told the club's faithful: "The Club is officially out of administration. We said in March to put the champagne in the fridge. Today you have permission to pop the cork.
"This has only been possible because of you, the supporters of this great and proud club. Well done and thank you."
The administration process was formally completed when BDO lodged exit papers with officials at the Court of Session.
In a statement, Jackson added: "This has been a challenging and complex process which has, fortunately, had a successful conclusion. In entering into an administration you can never be sure of the outcome and it is often a case of dealing with the day to day issues whilst also pushing for the final goal of exiting administration.
"There have been many people involved with this process over the last year and many have lived and breathed every minute of this administration in their efforts to produce this result.
"I would again like to thank Ann Budge and her team at the club, the Foundation, the fans, Peter Duff and all at Morisons LLP for their outstanding legal advice and patience, as well as the staff at BDO who have all put up with a lot to ensure the great name of Hearts survives to fight another day."