Hammond told Sky News on Thursday: "The economy has taken a shock".
Tory MPs responded furiously to Mr Osborne's warning of an emergency budget prior to June's referendum, which he said would contain £30bn of spending cuts and tax hikes to shore up the UK's finances if voters backed quitting the EU.
Lesser-known than Johnson but at least as important to Britain's future is David Davis, the cumbersomely titled Secretary of State for Exiting the European Union. There will be an Autumn Statement in the normal way and then there will be a Budget in the normal way, he said.
In other developments tonight, Michael Fallon was re-appointed as Defence Secretary, while Mrs May's close ally and leadership campaign manager Chris Grayling was yet to be handed a new job and remains as Leader of the Commons for now.
After filling half a dozen of the top jobs Wednesday - including surprise choice Boris Johnson as foreign Secretary - May made new appointments Thursday, including Justice Secretary Liz Truss and Education Secretary Justine Greening.
Howard Archer, chief economist at IHS, said the options before the BoE ranges from quantitative easing or "printing money" to cutting rates.
Amid reports his predecessor George Osborne, who he previously worked with, was sacked from the role, he said he did not believe the change was a policy decision, but rather one to allow Mrs May to bring together a team to help "reunite" the country.
Hammond, dubbed "Spreadsheet Phil" in political circles, was a successful businessman before entering parliament. The plan was dubbed a "punishment Budget" by angry Brexiteers.
Asked about the former London mayor's new role, which means he is in charge of MI6, Mr Hammond told Today: "The Cabinet works collectively and we have got a range of different characters and a range of different styles and a range of different talents".
He told BBC Radio 4's Today programme: "We will face some challenges in the short term in managing the economy".
While the selection of pro-Brexit campaign leader Boris Johnson as foreign minister dismayed some, Mr Hammond was seen as a good choice as chancellor of the exchequer. He told MPs: "Until we have served an article 50 notice, we remain a full, participating member of the European Union and our ability to negotiate new trade agreements is restricted by the continued application of European Union law until we have negotiated our exit from the EU".
Mr Hammond has been a loyal backer of Ms May throughout her campaign to succeed David Cameron, who stood down from office this afternoon. He resigned from his previous cabinet position as defence secretary in 2011 and voted against same-sex marriage in 2013. "We will take whatever measures are necessary to restore confidence, stabilise the economy as we move forward with the negotiating process".