The First Minister said he admires "certain aspects" of Mr Putin - but does not approve of a range of Russian actions - in an interview with Alastair Campbell, the former Labour strategy director, given on March 14.
He offered the view as Russia was being accused of military aggression over the future of Crimea, which it has since annexed, in neighbouring Ukraine.
The wider interview, including views on the future of Scotland and the independence campaign, will be published in GQ magazine on May 1.
Mr Salmond singled out German chancellor Angela Merkel for praise, saying she is "pretty effective".
And he remarked that while he admires US president Barack Obama's campaigning, he wondered why he could not have "done more".
Asked about Mr Putin, Mr Salmond said: "Well, obviously, I don't approve of a range of Russian actions, but I think Putin's more effective than the press he gets I would have thought, and you can see why he carries support in Russia."
Pressed on whether he admires the Russian leader, the First Minister said: "Certain aspects. He's restored a substantial part of Russian pride and that must be a good thing. There are aspects of Russian constitutionality and the inter-mesh with business and politics that are obviously difficult to admire. Russians are fantastic people, incidentally, they are lovely people."
He spoke warmly of Ms Merkel.
"I think the German Chancellor is pretty effective. Some chancellors have been unwilling to use German authority. She is not in that mould," he said.
Closer to home, he said Ukip leader Nigel Farage has a "certain bonhomie" - but said it is "not enough".
Mr Salmond continued: "He is having influence beyond his significance so you have to admire that. There is a constituency for saloon-bar politics and he has played it out. I have a sneaking regard for anyone who takes on powerful establishments."
On more domestic issues, Mr Salmond said he expects turnout in the Scottish independence referendum to be around 75% or higher.
The Scottish National Party leader also underlined his commitment to securing a currency union with the rest of the UK and talked about the Scottish Government's attempt to tackle the country's relationship with alcohol.
In the GQ interview Mr Salmond defends his support for minimum pricing, saying that he promotes the export of Scottish whisky around the world "(and) my argument is that if you are promoting it as authentic and of great worth, you cannot promote it from a nation of drunks."
A spokesman for the First Minister said: "The First Minister was very happy to take part in an interview for GQ - one of the best-read magazines in the country - and was perfectly happy with it being conducted by Alistair Campbell.
"The interview was conducted on March 14 but the First Minster correctly forecast that the Yes campaign was gaining ground in campaign and argument. This has been confirmed subsequently by all recent polls."
A spokesman for the First Minster said the interview was conducted before the annexation of the Crimea.
"Since then, the Scottish Government has made our position abundantly clear on the illegal annexation, including the decision to withdraw the invitation to the Russian Consul General to the annual Scottish Consular Corps dinner," he said.
Scottish Labour's external affairs spokeswoman Patricia Ferguson said: "Given he shares Nigel Farage's politics of division and grievance, it's hardly a surprise that the First Minister has found common ground with the Ukip Leader.
"But his comments about Vladmir Putin are insensitive and ill-judged given the precarious situation in Ukraine.
"For Scotland's First Minister to admit his admiration for someone with such a controversial record on human rights and democracy does not reflect well on our country."
Scottish Conservatives MSP Jackson Carlaw said: "Putin is keen on suppressing the media and political opposition, so it's no wonder Alex Salmond admires him.
"This is quite an embarrassing ramble from the First Minister, who is desperate to be seen as some kind of equal to global leaders.
"It also makes a mockery of the Scottish Government's faux outrage over the Crimea situation. The people of Scotland will see through this most recent sucking up offensive."