Liverpool have completed the signing of Netherlands midfielder Ryan Gravenberch from Bayern Munich ahead of Friday's transfer deadline, the clubs announced.

ESPN reported Thursday that the two clubs had agreed a fee of 40 million ($43.4m) for the 21-year-old.

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The transfer was briefly thrown into doubt on deadline day when Bayern's proposed move for Fulham midfielder João Palhinha fell through but Liverpool were able to get it over the line.

Gravenberch won the Bundesliga title in his only season with Bayern after signing from Ajax last summer.

He arrives at Anfield as Liverpool's fourth signing of the summer and will bolster a midfield that has seen the departures of several key players.

Naby Keita, James Milner and Alex Oxlade-Chamberlain all left following the expiration of their contracts, before manager Jurgen Klopp was dealt an unexpected blow with the loss of experienced duo Jordan Henderson and Fabinho to the cash-rich Saudi Pro League.

Liverpool have struggled to secure replacements, having agreed fees to sign Moisés Caicedo and Romeo Lavia before both instead decided to join Premier League rivals Chelsea.

Still, Klopp's side did get early deals for Alexis Mac Allister and Dominik Szoboszlai over the line before the arrival two weeks ago of Japanese midfielder Wataru Endo from VfB Stuttgart for a reported 16 million ($20.33m) fee.

Gravenberch has made 34 appearances for Bayern, but started just three games in the Bundesliga. He has 11 caps for the Netherlands.

Liverpool have taken seven points from their first three Premier League fixtures this season and next take on Aston Villa at Anfield on Sunday.