The 28-year-old Netherlands international arrives at Feyenoord as a free agent having ended his contract with Dynamo Moscow after just one year.
Bakkal had been in the sights of Feyenoord boss Ronald Koeman for some time after his successful loan spell at the club in the 2011-12 season, in which he scored 10 goals in 31 appearances.
Bakkal's efforts helped Feyenoord to second in that season, and after completing a medical on Monday, he said that he was delighted to be back.
"For me, it's especially important that I get a lot of games to come to a club where I feel good," Bakkal told the club's official website.
"It is a privilege to be at the club where we had a great season two years ago.
"Feyenoord have a good team, so I am confident that we can have another fantastic year."
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