The move is seen as a challenge to Volodymyr Zelensky, the former comedian elected president this weekend.
In a Facebook post, Mr Zelensky's team labelled Russia "an aggressor state which wages war against Ukraine".
Mr Putin said the new law was "purely a humanitarian issue".
The decree is aimed at people living in the unrecognised, self-styled republics of Donetsk and Luhansk, seized by Russian-backed separatists in 2014 after Russia annexed Crimea from Ukraine.
Mr Putin said people living in those areas were "completely deprived of civil rights" and could not "move normally" or "realise their most elementary needs".
"We have no desire to create problems for the new Ukrainian authorities," Mr Putin added.
What has the reaction been?
Ukraine's Foreign Minister Pavlo Klimkin labelled the decision a "continuation of aggression and interference in our internal affairs" and urged the residents of eastern Ukraine not to accept the passports.
In a Twitter post, he told them: "Russia has deprived you of the present, and now it is trespassing on your future."
Hopes for a fresh start killed off by Russia
Analysis by Jonah Fisher, BBC News, Kiev
There had been a school of thought that the election of Volodymyr Zelensky might bring fresh life to efforts to solve the conflict in eastern Ukraine. During the campaign he'd made vague if slightly conciliatory noises about the important of dialogue and talks.
Russia seems to have killed any prospect of that.
First, Moscow held off from congratulating Mr Zelensky for his landslide win.
Then just three days after the vote, Vladimir Putin announced he would give Russian passports to people regarded by everyone bar Russia as Ukrainians living on Ukrainian soil. In Kiev it's being seen another step towards eventual Russian annexation.
Mr Zelensky has been left with no choice. He's issued a statement condemning the Russian move and calling for increased pressure through diplomacy and sanctions. It's the sort of wording we've become used to seeing in the last five years from Ukraine. The fact that this time it has come from Mr Zelensky suggests that relations are unlikely to improve.
Iryna Gerashchenko, the deputy speaker of the Ukrainian parliament, noted the timing of the announcement.
Mr Putin "always uses moments of uncertainty and transition periods to plunge another knife into Ukraine's back", she said.
