He said that he will have no choice but to leave his post and return to the backbenches as he cannot sign up to support Mr Johnson's stance on accepting a No Deal Brexit.
Asked on the BBC One's Andrew Marr Show if he thought he would be sacked, Mr Hammond said: "No, I'm sure I'm not going to be sacked because I'm going to resign before we get to that point.
"Assuming that Boris Johnson becomes the next prime minister, I understand that his conditions for serving in his government would include accepting a no-deal exit on the 31st October and it's not something that I could ever sign up to.
"It's very important that the prime minister is able to have a chancellor who is closely aligned with him in terms of policy and I therefore intend to resign to Theresa May before she goes to the Palace to tender her own resignation on Wednesday."
Mr Hammond, a remainer, yesterday threatened to try to bring down a Boris Johnson government to block a No Deal Brexit.
In a hard-hitting interview with French paper Le Monde, he was asked repeatedly if he would vote no confidence in the next government if it pursued No Deal.
Refusing to rule out that course of action, he said: "I will argue there is no EU exit without Parliament's approval."
When asked explicitly if he would vote down Boris's government, he added: "I do not exclude anything at the moment."
Independent MP Nick Boles, who left the Conservatives this year because the party was "incapable of compromise" on Brexit, has praised Philip Hammond's decision to resign as Chancellor.
"Philip Hammond has discovered his irreducible core, the point past which he cannot be pushed," Mr Boles tweeted.
"If only others had the same commitment to their principles."
Mr Hammond has previously acknowledged that he would likely have no option but to step down as Chancellor if Mr Johnson becomes leader.
Mr Hammond said: "I will remain a member of the House of Commons. I will do everything in my power from my position to make sure that Parliament blocks a Brexit without agreement."
Mr Hammond's announcement that he plans to step down comes after Justice Secretary David Gauke - a former Remainer - told the Sunday Times he would also quit on Wednesday if Mr Johnson enters Number 10.
Mr Gauke said: "Given that I've been in the Cabinet since Theresa May came to power, I think the appropriate thing is for me to resign to her."