"Diego Lopez is very important," Inzaghi, who was celebrating his 41st birthday, said on Milan's website.
"He is an experienced goalkeeper and will improve our squad," added the former Milan and Italy striker.
“I’m very happy. The news has made my day.
“I think the signing will improve the group. Milan are making things better. This arrival is very important.”
Lopez is expected to sign a four-year, €2.5m-a-season contract at San Siro. Inzaghi did not provide details of the deal.
The 32-year-old is surplus to requirements at Real after the European champions signed Costa Rica keeper Keylor Navas from Levante this month.
Lopez, who played for Real as a teenager, was brought in as cover for injured captain Iker Casillas in January last year following stints at Villarreal and Sevilla.
He remained first choice at Real in La Liga last season, with Casillas playing in the Champions League and the King's Cup as part of an awkward rotation policy.
A former reserve keeper for Spain, Lopez made one substitute appearance for the European champions in August 2009 in a friendly against Macedonia.
- Sports & Recreation
- Iker Casillas