The Bavarians are thought to be on the verge of signing the Switzerland international, who is expected to sign a four-year contract with the club in the coming days
According to Bild, the two clubs have agreed a fee of 9 million euros for the 20-year-old winger which will rise if the player meets certain performance-based targets.
The paper claims that the Switzerland international, who will arrive at the Allianz Arena in the summer, will put pen to paper on a contract which will tie him to the Bavarians until 2016.
Bayern has been linked with Shaqiri for some time but Jupp Heynckes' side had initially set its sights on Borussia Monchengladbach star Marco Reus only for the Germany international to decide upon a summer switch to Borussia Dortmund instead.
Shaqiri's agent recently claimed Bayern would be the ideal destination for his client, citing that the player's development could only continue abroad. Earlier this month, the 20-year-old's former coach, Thorsten Fink, recommended Swiss starlet to the Bayern board.
Shaqiri will line up against Bayern later this month when Basel locks horns with the Bundesliga outfit in the last 16 of the Champions League.