The California-based iPhone maker said the song recognition tool would now soon be offered ad-free to all users.
Apple said last December that it was to buy London-based Shazam in a deal which reportedly valued the company at $400m (£300m).
But the takeover was held up by an in-depth probe by the European Commission.
However the EC cleared the deal earlier this month after finding that it would not give Apple a unique advantage over rivals such as Spotify - the market leader in the streaming market.
Apple announced on Monday that the deal had been completed.
Oliver Schusser, vice president of Apple Music, said: "Apple and Shazam have a long history together.
"Shazam was one of the first apps available when we launched the App Store and has become a favourite app for music fans everywhere."
Apple added: "The app will soon offer its experience ad-free for all users so everyone can enjoy the best of Shazam without interruption."
Shazam, founded in 2002, allows users to identify songs by pointing a smartphone or tablet at speakers playing music.
It employs about 250 people.
Apple said Shazam has been downloaded more than one billion times around the world and that users identify songs using the app more than 20 million times every day.