The HS2 high speed line will go to Euston, Transport Secretary Louise Haigh signalled on Tuesday.
She said an announcement would be made soon, expected at the October 30 Budget.
There had been speculation that HS2 trains running from Birmingham could stop at Old Oak Common in west London rather than Euston being the terminal given the soaring cost.
Pressed whether it was affordable for the high speed line to run to Euston, Ms Haigh told Times Radio: “It would never have made sense to leave it between Old Oak Common and Birmingham.
“Euston was always planned to be part of the picture for HS2. We are hoping to make an announcement on that very soon.”
She also stressed that the decision to turn off the huge advertising boards at Euston had proved “popular”.
Rail chiefs have come under fire for the state of the major rail terminal.
“I asked Network Rail to make those changes because the passenger experience was clearly not good enough there and they made the decision to temporarily turn off the advertising boards which has been very popular with customers,” explained Ms Haigh.
London business leaders are warning that the HS2 extension to Euston is vital and are urging the Chancellor Rachel Reeves to “get on board” the huge infrastructure project.
Last year then Prime Minster Rishi Sunak cancelled the Birmingham to Manchester leg of the scheme as costs soared.
When the expected bill for the rail project in the capital jumped to nearly £5 billion, there were reports trains would have to terminate at Old Oak Common in west London and passengers forced to continue their journey into Euston via the Elizabeth Line.
But now new Chancellor Rachel Reeves is expected to sign off the link running to north London despite the multi-billion pound price tag.
It is not yet clear how the line to Euston will be funded, with the previous Tory administration having sought to do so with private finance.
John Dickie, chief executive of London business group BusinessLDN, recently wrote to rail minister Lord Hendy stressing that not completing the project would risk the area losing £41billion in economic output and thousands of new homes.
He emphasised: “The design of the tunnels has been agreed and tunnel boring machines contracted, with one already on site and the second expected soon…Given costs already incurred, and with existing infrastructure and site teams in place, there will never be a cheaper time to build this tunnel than now.
“If the decision is further delayed it would lead to significant remobilisation costs.
“Failure to complete this section would further curtail North-South capacity and reduce the future value of HS2 as a key national infrastructure asset.”
Shadow education secretary Damian Hinds said the cost of extending HS2 to Euston must be a key consideration.
He told Times Radio: "It is really important that we get transport infrastructure right, clearly.
"But clearly that also has to be weighed against cost.
"And one thing we know about this Labour Government in its rather chaotic early days is that the numbers just are not adding up.
"And clearly they are going to have to think very, very long and hard about what they can spend on and indeed how they're going to raise money."
