Umaniec, an artist who co-founded an artistic movement known as "yellowism", was arrested on Monday and charged on Tuesday night after the mural was vandalised on Sunday.
He is alleged to have stepped over a wire barrier in the art gallery and daubed the Rothko mural, described as "priceless", with his name and the words "12 a potential piece of yellowism" before fleeing.
The gallery was then put into "operation shutdown" with people prevented from leaving or entering the building.
Paintings by Russian-born artist Rothko often fetch tens of millions of pounds. Earlier this year, his Orange, Red, Yellow sold for £53.8 million - the highest price paid for a piece of post-war art at auction. The 1961 painting went under the hammer at Christie's in New York.
The defaced painting, called Black On Maroon, was donated to the Tate in 1969 by Rothko himself.