"Now is the time for all of us to come together to find real solutions to the problems we face as a country," Hogan said in a statement that promised to work with Trump.
"For the past two years, our administration has been committed to working with both Democrats and Republicans to change Maryland for the better and that is exactly what we need to see more of in Washington, D.C.," the statement said.
"As we move forward, I encourage both parties to leave behind the divisive politics that have marred this election season and our nation for far too long and focus on doing what is best for America."
Hogan had distanced himself from his party's nominee during the primary and general election, saying he wasn't a fan of the brash real estate developer and would not vote for him. The governor skipped the Republican National Convention this summer, and on his ballot wrote-in his father's name as a presidential candidate instead.
Hogan had endorsed his friend New Jersey Gov. Chris Christie in the Republican presidential primary, but when Christie dropped out and endorsed Trump, Hogan said his support did not translate. Christie is expected to play a role on Trump's transition team.
Throughout, the governor repeatedly said he was disappointed in national politics and both Trump and Democratic nominee Hillary Clinton.