The 31-year-old was forced to miss Bayern Munich's opening Bundesliga fixture against Hoffenheim on Saturday due to a swollen ankle.
But he was put through his paces in Frankfurt last night and showed no adverse effects this morning, enabling him to join the 19-man squad for the clash in Baku.
Germany coach Joachim Low therefore decided against calling up Bayer Leverkusen striker Stefan Kiessling to provide extra cover following Lukas Podolski's withdrawal from the squad at the weekend.
He has Klose, Mario Gomez and Cacau available to lead his attack in Wednesday's qualifier, in which a victory would see Germany open up a four-point advantage over Russia at the top of Group Four.
Captain Michael Ballack was also on board, despite missing his flight over to Germany last night.
The Chelsea midfielder was caught up in traffic on his way from Wembley Stadium to the airport last night following his team's Community Shield victory over Manchester United, and was forced to return home before taking the first available flight out of London for Frankfurt this morning.
He arrived in time to link up with the squad for their four-and-a-half hour flight to Azerbaijan.