Russian President Vladimir Putin has agreed to buy billions of dollars worth of Ukrainian government bonds and slash the price Ukraine pays for Russian gas.
The announcement comes as Russia tries to stop Ukraine moving towards the EU.
Opposition leader Vitali Klitschko told pro-EU protesters in Kiev Mr Yanukovych was betraying Ukraine's independence.
"He has given up Ukraine's national interests, given up independence," Mr Klitschko, a former boxing champion, told the crowd on Tuesday.
"[President] Yanukovych used our country as collateral. According to our sources, he has agreed to a bailout from Russia and put Ukrainian plants, strategic industries, heavy industries, aviation and energy manufacturers up as collateral against it. We want to know what exactly he did put up as collateral, and his reasons for doing it."
He called on the Ukrainian president to hold a snap election.
"Yanukovych said at our round-table talks that he is not afraid of an early election. If that's the case, let him prove it in an honest fight," he said.
Although details of the agreement are unclear, Oleh Tyahnybok, leader of an opposition far-right group, said Mr Yanukovych had "pawned whole sectors" of the country's economy to Russia.
Ukraine urgently needs to cover an external funding gap of up to $17bn (£10.4bn; 12.3bn euros) next year to avoid defaulting on its debts.
After talks between Mr Putin and Mr Yanukovych in the Kremlin, it was announced Russia would buy $15bn-worth of Ukrainian government bonds.
The cost of Russian gas supplied to Ukraine has been slashed from more than $400 (£245; 291 euros) per 1,000 cubic metres to $268.5.
Mr Putin said the assistance was not "tied to any conditions".
He also said they had not discussed Ukraine joining a Moscow-led customs union with Belarus and Kazakhstan.
The US has warned the Ukrainian government that the deal with Russia would not satisfy the protesters.
German Chancellor Angela Merkel said ties with Russia should not prevent Kiev from looking West.
"At the moment it seems to be an either-or proposition. We need to put an end to this," she told ARD TV.
"A bidding competition won't solve the problem."
Mr Yanukovych made a surprise U-turn on an EU association agreement deal last month, sparking mass demonstrations.
He admitted his decision had been influenced by heavy pressure from Russia.
The current protests, the largest since Ukraine's 2004 Orange Revolution, are pushing for the resignation of Mr Yanukovych and his government, and early elections.
Ukraine relies on imports of Russian gas and heavy energy-intensive industries in eastern Ukraine are especially anxious to keep the price of gas down.
Some 75% of Ukraine's engineering exports go to Russia.
The agreement signed between Russia's Gazprom and Ukraine's Naftogaz amends a controversial 2009 deal signed by former Ukrainian Prime Minister Yulia Tymoshenko, for which she was jailed two years ago.
It's decision time for Ukraine's opposition leaders and for the pro-EU and anti-government protesters.
Do they continue to occupy Kiev's Independence Square - or Maidan - and government buildings, or do they pack up camp, dismantle the barricades, and wait for another incident around which they can build a mass civil disobedience campaign?
So far, although they have undoubtedly won a number of battles, they seem to have lost the war - or at least, a major theatre of conflict.
President Yanukovych has followed through on his intentions, enunciated at the outset of the standoff, that he would draw Ukraine closer to Russia.
Moreover, Prime Minister Mykola Azarov is still firmly in office, despite opposition demands for his ouster, and the country is no closer to early elections than it was four weeks ago, when the protests started.
Opposition leader Arseny Yatseniuk spent a large part of his speech on Tuesday evening describing the achievements of the "Euromaidan" movement - as if he were ready to declare victory and head home waiting for the 2015 presidential elections.
The only question remaining is if the students and other diehard activists who have occupied the Maidan during all these frigid weeks are willing to follow him.
Source: BBC News