The decree applies to anyone participating in military activities in Ukraine, assisting the army and serving in territorial defence units.
He signed the decree on Friday, with immediate effect.
It comes two days after Wagner leaders were presumed killed in a plane crash.
In a separate development on Saturday, a far-right subunit of Wagner, known as Rusich, said it was stopping military operations in Ukraine.
In a Telegram post, Rusich accused Russia's foreign ministry of failing to protect a founding member of the group, Yan Petrovsky, who has been arrested in Finland for visa violations and is facing extradition to Ukraine.
Analysts suggest Mr Putin's decree is part of attempts to reassert his authority following Wagner's mutiny in June.
"Putin wants to have tighter control on Wagner to make sure he won't be facing another crisis in the future," Natia Seskuria of Royal United Services Institute, a London think tank, told the BBC.
The decree comes as Wagner mercenaries are lacking an obvious leader, after a plane presumed to be carrying Yevgeny Prigozhin and other leaders crashed on Wednesday, killing all 10 people on board.
Described in the decree as a step to build the spiritual and moral foundations of Russia's defence, the oath includes a promise to strictly follow the orders of commanders.
"It is a concealed message to military intelligence to find and prosecute Wagner fighters," Petro Burkovskyi, who heads the Democratic Initiatives Foundation, a think tank based in Ukraine, told the BBC.
And it is a clear message to the fighters, too, he suggests: "Either take the oath and keep your arms or disarm yourself. You obey or you go to prison."
A few weeks before Prigozhin's failed uprising in June, the Russian defence ministry gave mercenary groups until 1 July to sign army contracts.
Prigozhin refused to sign, because he did not want Wagner to operate under the ministry. Mr Putin backed the ministry's contract scheme, which was the first public blow against his long-term ally Prigozhin.
The row escalated, leading to Prigozhin's mutiny.
But what effect will the decree have on the Wagner fighters without an obvious leader?
Mr Burkovskyi thinks that as experienced servicemen, they are good assets for the Russian army.
"They chose Wagner because Wagner gave them special treatment, without the bureaucracy of the huge Russian army. If they get special treatment under Putin's orders, I don't think they care about where, to whom and for whom they will fight."
Ms Seskuria believes that although the decree may have an effect in the short term, there are loyal Prigozhin supporters who will not take the oath.
"This can potentially create problems for Putin in a longer term-perspective," he says.
Meanwhile Russian air defences prevented drones attacks on Moscow and Belgorod regions on Saturday morning, officials said.
In the Belgorod region bordering Ukraine, four people were wounded by shelling, the local governor said.
The Ukrainian government almost never publicly admits carrying out for attacks inside Russia.
And in Ukraine, two people were killed and one wounded as Russia shelled a Ukrainian village near the north-eastern town of Kupiansk, Kharkiv's regional governor said.