The 26-year-old New Zealander signed for the Super Rugby side in 2012 and played a prominent role in their 2016 championship-winning season. He also skippered the team against the British and Irish Lions earlier this year.
"I'm really excited for the new opportunity to join Wasps," said Shields. "I think the club plays a similar style of rugby to the Hurricanes and feel I will fit in nicely. The club competes well across all the competitions and it's going to be the perfect place for my young family to settle."
Director of rugby Dai Young said Shields would be a valuable addition to the squad.
"We are looking forward to seeing the impact he can make for Wasps as he takes on the new challenge of the Aviva Premiership and European Rugby Champions Cup," he said.
"Alongside his natural talent, Brad is recognised for his immense physicality and high work-rate. He has made a number of eye-catching performances, particularly at number 8, but his versatility to play at 6 will also be beneficial to the squad."