After a month in limbo, Leonardo's contract has been terminated after Gian Piero Gasperini was announced as their new manager last week.
The Brazilian had a year left on his contract but has left to take over as sporting director at Paris St Germain, a move that had been mooted for several weeks.
Inter released a statement which read: "After six intense months and a Coppa Italia won together, Inter and Leonardo have terminated the Brazilian's contract on friendly terms.
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"Everyone at Inter continues to have the utmost esteem for a person capable of repeatedly taking on new challenges.
"President Massimo Moratti and everyone at the club thank him for what has been achieved together and wish him the very best of luck for the next stage of his career."
The former AC Milan coach was only at Inter for six months but achieved a runners-up spot in Serie A and a Coppa Italia.
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