The former Germany captain believes the Bavarians have pulled off a major coup by landing the prolific Poland striker on a free transfer from rivals Borussia Dortmund.
The Poland international will join up with Pep Guardiola's side once his Borussia Dortmund contract expires during the summer, with the 25-year-old following in the footsteps of Mario Gotze in swapping Signal Iduna Park for the Allianz Arena.
The switch looks set to cement Bayern's position as the dominant force in the Bundesliga, prompting Matthaus to praise the club's recent transfer activity.
"The Lewandowski move is a king transfer for Bayern," the former Germany captain told reporters. "But every transfer they have made over the past two or three years has been very useful.
"Previously, there were a couple of bad investments, but since then the purchasing policy has changed and all arrivals have either had experience of the Bundesliga or the coach has specifically asked for them."
Matthaus also believes the Lewandowski capture will cause further deterioration in the relationship between Bayern and Dortmund.
"Too much has happened with Lewandowski, Gotze and other disputes between the two clubs," he conceded. "The relationship is professional and co-operative but far from super."