The original 1991 John Currin portrait was recently sold at auction for $1.9 million to an anonymous buyer.
"Biggest surprise of my life. Thank you @JimmyKimmel -- the most generous guy in the world!" Ross tweeted Friday.
"@RealJeffreyRoss Bea is watching over us, but especially you," Kimmel tweeted back.
The Hollywood Reporter said representatives for Kimmel and Ross did not respond to its requests for comment on the generous gift.