The bank said in a statement the share sale would give it a strong enough "capital buffer" to withstand EU bank stress tests in the current climate of "high uncertainty and limited visibility".
The increase will also allow the lender to speed up a restructuring plan, due to be completed by 2017, that includes 8,000 job cuts and the closure of 550 branches.
The Tuscan bank has to pay back by the end of the year some €4.0 billion in credit it received from the Italian government last year to stave off bankruptcy.
Chief executive Fabrizio Viola told Italian news channel SkyTG24 that the share sale would be carried out "starting in mid-June until mid-July".
The larger-than-expected raising will also put the bank out of risk of being nationalised, he added.
Instead, Monte dei Paschi said the share sale would put it in a better position to seize "opportunities linked to a possible recovery of macro-economic conditions".
Investors cheered the news, with the bank's share price rising 2.81 percent to 0.2375 euros after the move.
Friday's board meeting also called an extraordinary meeting of shareholders for May 20-22 that will have to give its own approval for the capital increase.