The 20-year-old Slovakian keeper is to move to Tannadice on a three-year contract, subject to gaining international clearance.
"Filip is a highly promising young keeper," Tangerines boss Peter Houston told the official Dundee United website.
"That he's been at Manchester City for the last few seasons confirms his credentials.
"Obviously he's found it difficult to break through there given their presence in the transfer market these days."