Lewandowski is expected to cost EUR 50 million and sign a three-year deal with the Spanish giants, subject to undergoing a medical, news outlets reported.
The Polish striker, 33, had one year remaining on his Bayern contract but told the German club in June that he wished to continue his career elsewhere.
Lewandowski had played in Munich since 2014, a success-laden eight years that launched him to the top of world football.
He scored 344 times in 374 games for Bayern, helping the club to eight German titles and the 2020 Champions League.
'These eight years were special'
As the curtain fell on his spell with Bayern, Lewandowski told reporters on Saturday: "These eight years were special and you don't forget that. I had a great time in Munich."
He added: "I will fly soon but after the training camp I will come back and say goodbye properly and organise a few things. I said goodbye to the boys on the field today, I wasn't worried about an injury in training. Something can happen to me at home. I wanted to keep fit and trained with the boys again."
Meanwhile, Bayern President Herbert Hainer said: "It's good to have clarity for all parties. We have come to a verbal agreement with Barcelona."
Hainer added: "Robert is an incredible player and he won everything with us. We are incredibly grateful to him."
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Source: PAP, skysports.com, bbc.com