The 28-year-old announced his departure Saturday night following a meeting with Flamengo president Eduardo Bandeira de Mello, reports Xinhua.
Love denied the move was the result of a falling out with the football club.
"There have been reports in the media saying I am unhappy with the club but that is not true," Love told Brazilian daily O Globo.
"I received a request and we agreed to accept it, but I will leave with a heavy heart."
Love scored 79 goals from 158 matches in his first spell with the Russian club between 2004 and 2011.
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Bandeira left the door open for the forward to return to Flamengo in the future.
"I am a big fan of his and hope that one day I can welcome him back," Bandeira said.