Berlusconi has agreed to temporarily resign as prime minister and receive a new mandate from President Carlo Azeglio Ciampi, Fini said in a statement on Monday.
The government had been on the verge of collapse since the Union of Christian Democrats party (UDC) quit the cabinet on Friday.
The centrist party has agreed to return to a new administration in a move that would avert a collapse of the coalition and snap elections.
Senior UDC member Rocco Buttiglione on Monday said Berlusconi had agreed to resign and then form a new government, despite the prime minister's reluctance to avoid formal dissolution of his four-year-old administration.
On the brink
"The House of Freedoms has reached agreement on the main points," the former European affairs minister said, referring to Berlusconi's centre-right ruling coalition.
"We're heading for a second Berlusconi government along the lines indicated by our party."
Stagnant economy and infighting
have hurt Berlusconi's standing
Berlusconi's government seemed on the brink since the UDC walked out on Friday demanding major policy changes after the centre-right coalition suffered heavy losses in regional elections.
The row with the UDC and the need to step down, albeit briefly, before forming a new administration could weaken his political standing.
"A Berlusconi-2 would be akin to recognising that in four years of government the House of Freedoms has got everything wrong. It would be an enormous advantage to the UDC and the opposition," Turin's La Stampa daily said on Sunday.
The deal gives Berlusconi a year to improve the centre-right's electoral prospects, dented by a stagnant economy and the battering that the latest infighting has dealt to the its standing.
A fresh sign of the mountain Berlusconi has to climb was provided by voters in the small southern region of Basilicata in a regional election held on Sunday and Monday, two weeks after he lost 11 of 13 regions that went to the polls around the country.
The centre-left won Basilicata with some 70% of the vote, exit polls indicated, increasing its majority and taking the overall tally of regions to 12-2 in the centre-left's favour.