But the party’s leader did not commit to a timeframe for the move, stressing discussions are pending on when “exactly” it would come to pass.
The proposal forms part of Labour’s blueprint for a “New Britain”, outlined in the report of its commission on the UK’s future – headed by ex-premier Gordon Brown.
Sir Keir will hail the proposals for political and economic devolution as “the biggest ever transfer of power from Westminster to the British people” at a joint press conference in Leeds on Monday.
He had hinted that some of the measures – including a new democratic assembly of nations and regions to replace the Lords – may have to wait for a second term Labour government.
But quizzed repeatedly on when his party would enact the proposal to abolish the upper chamber during a broadcast round on Monday, he said he hoped to deliver the change within the first five years of governing.
Sir Keir suggested the move, along with all other proposals in the report, could be achieved within Labour’s first term.
“I’m very keen that all of the recommendations in the report are carried out as quickly as possible,” he told BBC Breakfast.
“So we will now have after today a process of consultation testing the ideas … with a view to how do we implement them?”
Pressed on whether he hoped to abolish the Lords in Labour’s first term, he told Sky News: “Yes, I do.
“Because when I asked Gordon Brown to set up the commission and do this, I said what I want is recommendations that are capable of being implemented in the first term.”
Mr Brown has insisted the current upper chamber is “indefensible” and has to go.
He warned in a briefing for Scottish journalists ahead of the report’s launch that the issue could “come to a head” when Boris Johnson publishes his resignation honours list, which is expected to include a number of new peers.
The former Labour leader said there was a feeling many in the Lords were there “simply because they have been friends with the Conservative Party and not because of their contribution to public policy”.
Among the report’s 40 recommendations is a call to give local communities new powers over skills, transport, planning and culture to drive growth.
The panel calls for a new constitutional law setting out how political power should be shared, with a requirement for decisions to be taken “as close as meaningfully possible” to the people affected by them.
There would be an explicit requirement to rebalance the economy to spread prosperity and investment more equally across the UK, and the right to healthcare based on need rather than ability to pay would be enshrined in a set of protected social rights.
Towns, cities and other areas would also be brought together as part of a co-ordinated economic strategy, with some 50,000 civil service jobs transferred out of London.
Meanwhile, the report advocates extra powers for Scotland and Wales, with restored and strengthened devolution in Northern Ireland.
The report also proposes a series of measures to clean up politics including a new anti-corruption agency, an integrity and ethics commission to replace the various existing “ad hoc bodies” and a ban on most second jobs for MPs.
Backing the plan, Sir Keir will tell the launch event: “The centre hasn’t delivered.
“We have an unbalanced economy which makes too little use of the talents of too few people in too few places.
“We will have higher standards in public life, a wider spread of power and opportunity, and better economic growth that benefits everyone, wherever they are.
“By setting our sights higher, wider, better, we can build a better future together.”
He will say the report reflects the demand from people across the country for a “new approach”.
“During the Brexit referendum I argued for Remain, but I couldn’t disagree with the basic case that many Leave voters made to me,” he will say.
“They wanted democratic control over their lives so they could provide opportunities for the next generation, build communities they felt proud of, and public services they could rely on.
“And I know that in the Scottish referendum in 2014, many of those who voted ‘Yes’ did so for similar reasons, the same frustration at a Westminster system that seems remote.”