The trio also agreed to limit the number of new players they could register in European competition, European football's governing body said in a statement following a decision by its financial control watchdog.
They were among 10 clubs, also including Sporting Lisbon, who came to settlements with UEFA after falling foul of the rules designed to stop clubs overspending.
Inter would pay "a total amount up to 20 million euros (£14.5 million)", Monaco up to 13 million and Roma up to six million, the exact amounts depending on a number of conditions, UEFA said in a statement.
In Inter's case, six million euros would be paid in full, to be deducted from the club's European competition revenue starting from the current season, while payment of the remaining 14 million was conditional.
UEFA said Inter would be allowed only 21 players, instead of 25, in their squad if they qualify for European competition next season, rising to 22 in the 2016/17 season.
Roma and Monaco would be allowed 22 players in their squads next season.
Sporting, Besiktas, FC Krasnodar and fellow Russian side Lokomotiv Moscow also came to similar settlements with UEFA.
CSKA Sofia, Kardemir Karabukspor and FC Rostov, who were guilty of minor infringements, were fined $200,000 each and agreed to meet break-even requirements by next season.
FFP rules, which limit club spending in relation to revenue, were introduced to prevent rich owners from pumping unlimited amounts of cash into teams and distorting the market.
Critics, however, say the new regulations have cut off any opportunity for smaller clubs to challenge the established teams for European dominance.
Last year, Manchester City and Paris St Germain, two of the newly rich clubs in European football, were fined up to 60 million euros and had their squads capped for this season's Champions League
They also pledged to curb transfer spending over two seasons.
(Writing by Brian Homewood in Berne; editing by Toby Davis and Ken Ferris)
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