"In the very near future, transit - and the Ukrainian side has assured us to this effect - will resume," said Mr Putin, speaking alongside his Ukrainian counterpart on Russian TV.
Mrs Tymoshenko said that the two countries' energy companies, Gazprom and Naftohaz, had been instructed to draw up the relevant contracts by Monday.
Mrs Tymoshenko said: "Immediately after all the documents on the transit and purchase of gas are signed, all the routes for gas transit and gas supplies to Europe will be restored.
"I believe today has been a fruitful day. Mutual understanding has been found."
The parties were under pressure from Brussels to reach a deal this weekend.
European Commission spokesman Johannes Laitenberger had said the Moscow talks offered "the last and best chance for Russia and Ukraine to demonstrate they are serious about resolving this dispute".
"The gas must flow," he added. "We will regard this period as a test case for judging whether or not they are credible partners."
EU states import a quarter of their gas from Russia and 80% of supplies come via Ukraine. Almost 20 countries in Europe have been affected by the dispute.
Russia switched off the gas this month, accusing Ukraine firstly of failing to pay for its own supply, then later of stealing gas meant for other countries.
Some central and east European states have been reduced to rationing gas, while others have been seeking alternatives to the Ukrainian pipelines.
The gas dispute created the EU's worst ever energy crisis, the BBC's Richard Galpin reports from Moscow.
At his news conference with Mrs Tymoshenko, Mr Putin said that discounts for both Russian gas supplied to Ukraine and the transit rate charged by Kiev would apply for the current year.
"We agreed that in 2009 our Ukrainian partners will have a discount of 20% on condition that the preferential tariff for piping Russian gas to European consumers through Ukraine in 2009 remains in force and that the price for piping will be the price of 2008," he said.
"We also agreed that from 1 January 2010 we will entirely move to price and tariff formation fully in accordance with European standards without any exemptions or discounts as regards both the transit and the price of gas."
European-level prices for gas supplies will mean, at current rates, a jump from $179.5 per 1,000 cubic metres to $380 for Ukraine, according to the Kremlin.
On the eve of the talks, sharp divisions emerged between Ukraine's president and prime minister, political foes in a fragile coalition government.
Mr Yushchenko's office insisted the Moscow talks must combine gas supplies to Ukraine with transit supplies to Europe in "a single package".
Mrs Tymoshenko for her part said: "The Ukrainian government does not link the issue of concluding an agreement on [Russian] gas supplies to Ukraine with the issue of resuming gas transit to Europe."
There was no immediate reaction to Saturday night's deal from Mr Yushchenko.
Russian President Dmitry Medvedev hosted an emergency gas summit in Moscow on Saturday but EU leaders heeded a call by the Czech Republic, which holds the EU's rotating presidency, to stay away in order for Brussels to speak with one voice at the meeting.
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