Inter - co-owned by former England captain David Beckham - are preparing for their first season in MLS in 2020.
The Florida club have reportedly paid Monterrey $12million for Pizarro after lengthy negotiations.
It was said Monterrey initially wanted $20m for the Mexico midfielder amid a complication with his release clause.
Pizarro scored in Inter's 2-1 defeat to Philadelphia Union on Saturday before the deal was belatedly finalised on Monday.
Inter have been linked with a host of big names from European football, including Edinson Cavani and Luis Suarez, and still have one remaining DP slot.
Beckham's team will make their MLS bow against Supporters' Shield holders Los Angeles FC on March 1.