Judge Roger Chapple, at Inner London Crown Court, told Umaniec: "Your actions on the 7th of October of this year were entirely deliberate, planned and intentional."
He said it was "abundantly clear" that Umaniec was "plainly an intelligent man" and told the court he had described Rothko as a "great painter" in a letter he had written to him.
The judge also said the incident had led to galleries reviewing security arrangements at a cost to themselves and the taxpayer.
"The effects of such security reviews is to distance the public from the works of art they come to enjoy," he said.
Gregor McKinley, prosecuting, said:
Sotheby's has given Tate Modern a verbal estimate of pre-damage value of approximately between £5 million to just over £9 million.
The work required to restore this picture will be complex and lengthy.
Complications to this work include the unique painting technique used by the artist and the fact the ink used by Mr Umaniec has permeated the paint layers and the canvas itself.
Mr McKinley said work to restore the painting will take about 20 months and cost "something around £200,000."
Gareth Morgan, defending, said it would take a "significant amount of effort, expert effort at that" to restore the "important, valuable piece of art".
Paintings by Russian-born artist Rothko often fetch tens of millions of pounds.
26 year old Wlodzimierz Umaniec - who's also known as Vladimir Umanets - has been jailed today for two years at Inner London Crown Court for defacing a Mark Rothko painting at the Tate Modern gallery.