The Switzerland centre-back has agreed a three-and-half-year deal, subject to governing body approval, for an undisclosed fee.
Matt Jarvis, Ivo Pinto and Ben Godfrey have already moved to Carrow Road this month as manager Alex Neil continues to bolster his squad.
"Norwich City are delighted to make their fourth signing of the January transfer window, completing a deal for Switzerland international defender Timm Klose from VfL Wolfsburg subject to governing body approval," said a Canaries statement.
Neil, who is also on the verge of adding a fifth new arrival, Everton forward Steven Naismith, is pleased to have added more cover at the back.
"Timm has got plenty of experience having played in the Bundesliga, in the Champions League and for his country, which will be an asset to us," he told canaries.co.uk.
"As a player, he's got good technical ability and he's solid in the air
He can also play at either right centre-back or left centre-back.
"We're delighted to have completed this deal and to have added Timm to our squad."
The 27-year-old defender, who played against Manchester United in the Champions League this season, is looking forward to a new career in England.
"It was always a dream to play in the Premier League and Norwich have given me a big chance," he said.
"Now I want to give everything I can to be a good player in this league.
"When I came here and saw the training ground, the stadium, and everything - it was fantastic."
Source : PA