The Cabinet Office minister announced the decision on Friday, adding: “The moment for extension has now passed”.
In a post on Twitter, Mr Gove said he had chaired a “constructive” meeting of the EU Joint Committee with EU Commission Vice-President for Interinstitutional Relations Maros Sefcovic.
He said: “I formally confirmed the UK will not extend the transition period & the moment for extension has now passed. On January 1, 2021, we will take back control and regain our political & economic independence.”
It comes after Nicola Sturgeon and Mark Drakeford, the First Ministers of Scotland and Wales, wrote to the Prime Minister on Friday calling on him to request the extension, saying it would be “extraordinarily reckless” to end the transition in the new year.
The vice-president of the EU Commission Maros Sefcovic has said Friday’s meeting of the EU-UK Joint Committee was “positive” but that there is still more to do.
Speaking at the European Commission press briefing, Mr Sefcovic said: “I have to underline that the meeting took place in very good atmosphere and I am glad that at the end of our discussions we also arrived at some positive results, which I believe would pave the way forward for the proper implementation of the Withdrawal Agreement.”
He added: “However, with some six months to go before the end of the transition period we still have lots of work to do.”
Mr Sefcovic added that this was particularly true with regards to the Northern Ireland protocol.
He said: “The window of opportunity to put in place the operational measures needed to ensure that the protocol can function as intended on January 1 2021 is rapidly closing.”
On the UK’s command paper on implementing the Northern Ireland protocol, he added: “We need to move from aspiration to operation and fast.”
Mr Sefcovic added that Mr Gove made it clear that the UK will not accept an extension to the transition period.
He said: “Michael Gove confirmed to me that the UK will not consider an extension of the transition period.
“From our side, I have taken note of the position of the UK on this issue and have stated, as President von der Leyen has already done, that the EU remains open to such an extension.
“In this context, we both, with Chancellor Gove, agreed on accelerating the implementation of the Withdrawal Agreement and to accelerate our work, and we also agreed that the Joint Committee should meet again in early September.
“By this date we also concluded that specialised committees including the one on the Ireland/Northern Ireland protocol will meet in the coming weeks.”
Mr Sefcovic added that he made clear to Mr Gove the need for the UK to uphold its commitments to Northern Ireland.
He said: “Only a sound and effective implementation of all these legal obligations can ensure continued peace and stability between all communities on the island of Ireland, uphold the Good Friday Belfast Agreement in all its dimensions while also preserving the EU single market, and I made these points to minister Gove very clearly.”
Mr Sefcovic added that it is up to the UK how it takes back control.
Responding to reports of the Government abandoning plans on full border checks for EU goods, he said: “This issue was not in particular discussed today and I would say that the UK has stated on several occasions that it wants to take back the control, and I would say it is up to the UK how they do it.
“What is of course very important for us is that at the end of the transition period the UK will decide how it wishes to organise its borders as a WTO member.”
He added that at the meeting, quite some time was spent “discussing the enormity of the task when it comes to the proper implementation of Ireland and Northern Ireland, and that we agreed that the acceleration of work is necessary”.
UK sources were keen to depict the meeting as the last formal opportunity to request an extension to the transition period, as it is the last scheduled meeting of the joint committee before the July 1 deadline.
But both sides can agree to hold another such meeting, where under the Withdrawal Agreement a delay could be asked for.
Boris Johnson has repeatedly insisted he will not ask for a delay, despite businesses and critics warning of the dangers of a departure without a trade agreement in place.
A virtual summit between the Prime Minister and EU chief Ursula von der Leyen to try to break the deadlock in trade negotiations has been scheduled for Monday.
The negotiating teams have also agreed to “an intensified timetable” for July with possible discussions in person if public health guidelines enable them during the coronavirus pandemic.
European Council president Charles Michel and the president of the European Parliament, David-Maria Sassoli will also join the political talks.
The pace of talks will be scaled up so negotiators will meet in each of the five weeks between June 29 and July 27, No 10 said.
EU chief negotiator Michel Barnier lamented there having been “no significant areas of progress” as he accused the UK of having “backtracking” on the agreed political declaration.
His counterpart in Downing Street, David Frost, said they would have to “intensify and accelerate” the process if there was to be any chance of an agreement.
Both sides also said the remote meetings had reached their limit and that face-to-face meetings would be needed in order to progress.