The No. 4141 Engine led the Bush funeral train from Houston to College Station in December 2018, when the former president was laid to rest at alongside First Lady Barbara Bush.
According to Texas A&M, Union Pacific announced that it would donate the locomotive to the museum a year later.
The railroad surprised Bush in 2005 by painting it to resemble Air Force One, Texas A&M said.
Texas A&M University said Dick Davidson, the former CEO of Union Pacific, and his wife, Trish, made a significant gift to jumpstart private fund-raising for the museum expansion.
"It is fitting this significant piece of history will now make its permanent home at the Bush Center at Texas A&M," Max Angerholzer, CEO of the George and Barbara Bush Foundation, said. "The train meant the world to President Bush. We are grateful to the entire Union Pacific team, especially Chairman and CEO Lance Fritz, for this special gift."