— ПФК ЦСКА Москва (@pfc_cska) August 5, 2020
CSKA have paid €8.5m for Gaich and San Lorenzo inserted a 20 per cent sell-on clause into the deal.
The towering forward has penned a five-year deal with CSKA and has a €30m release clause.
Gaich leaves San Lorenzo after scoring seven times in 27 appearances.
He won his first and to date only cap for Argentina last September as a late substitute against Mexico.