Prosecutors decided last month to ask a court to dismiss charges against Lagarde, her lawyer Yves Repiquet told the Reuters news agency Wednesday.
The IMF boss was a minister in Nicolas Sarkozy's government in 2008, when the payout took place.
She was charged with "negligence by a person holding public authority" on 27 August 2014 because she sent the dispute between Tapie and the Crédit Lyonnais bank, whose assets were managed by a state-owned consortium at the time, to arbitration.
The decision led to the massive payout, even though Tapie, who was bankrupt at the time, could not have contested a decision by the consortium in court.
It has since been overturned, although Tapie is appealing and asking for a billion euros in compensation.
Despite having been a minister in a left-wing government, Tapie backed right-winger Nicolas Sarkozy in the 2007 presidential election, allegedly in return for a promise of help with charges of tax fraud he faced at the time.
Tapie and five other people face fraud charges in relation to the case.
One of them is Orange boss Richard, who worked for Lagarde at the time.
According to Le Monde newspaper, she has accused him of using a stamp of her signature on a key letter relating to the case.
Richard reportedly said she was kept up to date on all aspects of the case.
That could leave Lagarde in the awkward situation of having to testify against her former chief of staff.