He is expected to step down in October, while the new prime minister is set to be elected in September.
"Today I'm standing to be leader of the Conservative Party and to be prime minister… I love my country. I love my party," Crabb said at a press conference, as broadcast by the Sky News television channel.
He added that he would be running with Conservative member Sajid Javid, who would serve as his chancellor, while his Attorney General Jeremy Wright was at the moment his campaign manager.
Crabb stated that he was opposed to the idea of a second referendum on UK membership in the European Union.
"There can be no continuity Remain campaign to subvert the process of our exit from EU," Crabb stressed.
According to the politician, the United Kingdom should remain close to Europe, but the "supremacy of EU law" should end.