Bolton confirmed the deal on April 17 and the takeover will now be subject to English Football League (EFL) approval.
As part of the agreement, Bassini will secure full control of the hotel at the University of Bolton Stadium. He also confirmed that existing owner Ken Anderson will have no further involvement in the club once the EFL has given consent to the purchase.
Cash-strapped Wanderers have been relegated to League One, after losing to Blackburn Rovers 2-0. Players and other staff are still yet to be paid their March wages.
It is the second month in a row that wages have been late, causing team members to appeal to the Professional Footballers’ Association (PFA) for support.
The club narrowly avoided administration in September last year, with the threat only staved off due to former owner Eddie Davies loaning the club £5 million ($6.5m) days before his death.
Bolton have also twice appeared in the High Court over an unpaid tax bill, with the case being adjourned until May 8.
In a club statement announcing the takeover, Bolton said "significant funds" will be made available to pay outstanding wages and long-term creditors.
They added that "once completion has occurred, all the long terms debts to HMRC and suppliers will be settled".
The agreement comes after numerous failed attempts from Anderson to sell the club. The owner blamed a lack of cash from interested parties for deals falling through, before finally finding a buyer in Bassini.
The Stanmore-based businessman acquired Watford in 2011, before selling a year later. In 2013, he was handed a three-year ban from having any involvement in a position of authority with any EFL club due to misconduct and dishonesty over financial dealings during his time as Watford. He filed for bankruptcy in 2014, the second time in seven years.
Speaking to BBC Radio Manchester, Bassini said: “We worked very, very hard to get the deal done. It was very close, to going to administration this morning. At the 11th hour, we did it, going through the night.
“Now we have to look to restructure and move the club back up to where it belongs.”
In a statement, Anderson said: “I am very pleased to hand over ownership of this great club to Laurence, I wish him and all of our supporters the very best for the future.”