Lewandowski will fly to Spain on Saturday for a medical before signing a three-year contract with a 12-month extension option.
The Poland international had only one year left on his Bayern contract and had informed the club that he would not be renewing it.
Until now, the German champions have insisted Lewandowski is not for sale, rejecting a €40 million (£33.8 million) offer from Barcelona last month.
However, Lewandowski’s departure would allow Bayern to fund the signing of Matthijs de Ligt from Juventus, who are asking for around €80 million (£67.7 million) plus bonuses, according to Sky in Italy.
Bayern’s sporting director, Hasan Salihamidzic, was in Turin on Monday to begin negotiations with Juventus for De Ligt. The Dutchman has two years left on his contract with Juve and is said to have told the Italian club that he wants to move to Munich.
Chelsea has also been tracking De Ligt this summer as they look to replace Antonio Rudiger and Andreas Christensen, both of whom left on free transfers but are set to sign Kalidou Koulibaly.
Lewandowski has been with Bayern Munich since 2014, scoring 344 goals in 375 appearances across all competitions.
He has helped Bayern win eight Bundesliga titles in the last eight seasons, as well as three German Cups, and was recently named the league’s top scorer for the fifth season in a row, after scoring 35 goals in 34 Bundesliga games in 2021/22.
“Xavi is desperate for a world-class striker capable of scoring 30 or more goals per season.” A two- or three-year contract with a salary of €35m to €40m (£30m to £34m) per year is in the works.
“Barcelona cannot pay high fees but can pay high salaries.” Lewandowski’s dream has always been to play in Spain, preferably for Real Madrid or Barcelona.”