But former Ukip leader Mr Farage took a swipe back at Mr Baker and suggested he had not been consistent in his views on Brexit.
Speaking on his GB News show, the Brexit architect said: “It was very bizarre really.
“Steve Baker, I’m sure you’ve seen him on your TV screens, he’s terribly self-important and he sets himself up to be one of the great Brexiteers.
“That is of course until he gets a ministerial car, it’s amazing how people change once that happens.
“Yes poor old Boris Johnson did vote against the Windsor Framework. Perhaps he has become a pound shop Nigel Farage.
“But you see unlike you Mr Baker, I tend to be fairly consistent in my views when I believe in sovereignty.
“You yourself Mr Baker, in March last year, said we should trigger Article 16, we have to get the UK single market back and Stormont up and running.
“As I say, it’s amazing what a ministerial car will do.”
Referring to the European Research Group reportedly removing Mr Baker from one of their WhatsApp groups following his comments, Mr Farage added: “Never mind the ERG have kicked him out of their group I’m very pleased to say.”
And in a tweet, Mr Farage said: “You give Steve Baker a Government job and he stops being a Brexiteer.”
Mr Baker – an ardent Brexiteer who was influential in bringing an end to Theresa May’s premiership following Tory fury with her approach to EU negotiations – said Mr Johnson being viewed as a pale imitation of Mr Farage ahead of this afternoon’s first Commons vote on the Windsor Framework.
He said former PMs Mr Johnson and Liz Truss should “be backing the Windsor Framework today”.
Mr Baker, who previously chaired the powerful ERG of Conservative Brexiteers, said: “What I would say is they are both better than this.
“We’ve partly reached this point thanks to Liz Truss setting the process in train.
“And today’s measures are better, of course, than the protocol that Boris Johnson put in place, a protocol which he spoke about and those things turned out not to be accurate.
“So he has a choice: he can be remembered for the great acts of statecraft that he achieved or he can risk looking like a pound shop Nigel Farage.
“I hope he chooses to be remembered as a statesman.”
Mr Johnson and Ms Truss were among 22 Tory MPs who rebelled against the Government in the vote on the Stormont brake aspect of the deal.
The mechanism, designed to give a veto over the imposition of new EU rules in Northern Ireland, was passed by 515 votes to 29, with Labour and other opposition parties backing it.
Six DUP MPs voted against the statutory instrument along with former Tory Andrew Bridgen, who now sits as an independent, while more than 40 Conservative MPs did not vote – although some would have had permission to be away from Westminster.