Bassini had sought time last week to provide the English Football League (EFL) with proof of funds to buy the relegated Championship (second tier) club but Bolton said that nothing had been presented to the governing body to consider.
"Mr Bassini failed to provide any adequate and acceptable proof of current and future funding to the EFL... despite him telling the media he has the ability to perform since early March," Anderson said in a statement on the club's website.
Anderson said Bassini's "continued time wasting" and "empty promises" had left him with little choice other than to place the club into administration, with "any likelihood of finding any resolution the High Court hearing not possible."
"This had been a massive disappointment as I understand the serious implications administration will bring... but I have been left with no alternative, as this course of action will preserve the football club and all of its proud history."
A Football League founder member in 1888, Bolton won the FA Cup three times in the 1920s and in 1958 but have struggled in recent years after relegation from the Premier League in 2012.
The club's players had said they would boycott their final two games over unpaid wages, leading to the home match against Brentford being postponed and later called off.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
