Shakib is currently ranked as the top all-rounder by the ICC in one-day internationals and will join Australian Joe Burns at Grace Road.
Head coach Phil Whitticase said: "Shakib's record is exceptional and I am looking forward to him helping us to achieve success in the Friends Life t20 competition this year."
The 26-year-old - who had a previous spell in county cricket with Worcestershire - has scored 1,421 runs in 90 career T20 matches at a strike rate of over 120.
Shakib has also claimed 111 wickets at an average of 20.18, with an economy rate of 6.73.
- Sports & Recreation