Congress must now approve a package that includes spending cuts to avert a disastrous default after the White House agreement had been reached "in principle".
The deal, which would suspend the federal government's $31.4 trillion debt ceiling, was reached late on Saturday ending a month-long stalemate.
Mr McCarthy, the US Speaker, told reporters that the budget deal includes raising the debt limit for two years, until the next presidential election.
"This is going to be transformational, where Congress is literally going to spend less money," he said.
The deal also involves agreeing to a Republican demand to increase work requirements for recipients of the federal food-stamps aid programme, which Democrats were vehemently against, but stopped short of accepting the greater spending cuts for which the opposition had asked.
The details of the compromise are expected to be made public on Sunday evening.
The agreement “doesn't get everything everybody wanted”, Mr McCarthy said, which was expected given the divisions on the issue. “At the end of the day, people can look together to be able to pass this.
"We did a conference call with our conference and over 95 per cent were overwhelmingly excited about what they see."
On Sunday, Mr Biden praised the agreement he has reached with Mr McCarthy, saying: “It’s a really important step forward.
"It takes the threat of catastrophic default off the table, protects our hard-earned economic recovery and the agreement also represents a compromise which means no one got everything they want but that’s the responsibility of governing.
"As the Speaker and I made clear from the start, the only way forward was a bipartisan agreement.
"That agreement now goes to the United States House and to the Senate. I strongly urge both chambers to pass that agreement.
"Let's keep moving forward on meeting our obligations and building the strongest economy in the history of the world."
Mr Biden said Democrats who were worrying that he gave away too much in negotiations will "find I didn’t".
“I think he negotiated with me in good faith. He kept his word,” he said.
Mr Biden said expected Mr McCarthy to have enough votes to pass the deal.
A failure by Congress to reach a deal before June 5 could cause a US default that would be felt around the world.
Mr McCarthy said the agreement would be about 150 pages long and would be made available for the American public to see, adding that the House would wait 72 hours before voting on it.
"We wanted to be very open to the American public about what we were talking about," he said.
On Sunday, there were signs that both progressive as well as conservative representatives were displeased with the deal.
Pramila Jayapal, chairwoman of the House Progressive Caucus and a Democratic representative from Washington. said curbing social programmes was "very bad policy”.
“We are one of the only countries in the world, if not the only country in the world, that is an industrialised country that puts any requirements on people who just want food,” Ms Jayapal said told CNN about imposing stricter work requirements on government assistance programmes.
Republican Senator from Kentucky Rand Paul called the agreement "fake spending cuts" in a tweet.
"Conservatives have been sold out once again," he said.
Centrist Democratic representative from Connecticut Jim Himes told Fox News that he had not yet made up his mind about the bill.
“I’m going to listen to what the President’s and his people’s arguments are," Mr Himes said. "But no, I’m anything but a clear 'yes' vote at this point.”