Nadiya Savchenko, the Ukrainian air force pilot who was recently jailed in Russia for 22 years, was flown back to Kyiv to a hero's welcome on May 25 in a swap for two Russian servicemen captured in the eastern Donbas region.

Upon her return to Ukrainian soil, President Petro Poroshenko said his country will return Crimea, which was annexed by Russia in 2014, and separatist-held areas of the Donbas to Ukrainian sovereignty "like we have returned Nadiya".

While highlighting the tensions between the two countries about the continuing conflict in East Ukraine, the exchange removes one obstacle to efforts to normalise the situation, and also sheds a domestic irritant for both Poroshenko and his Russian counterpart Vladimir Putin.

Savchenko, 35, was jailed for allegedly assisting in the killing in 2014 of two Russian journalists in the Donbas conflict, a charge she rejects. Being regarded as a symbol of Ukrainian resistance to Russian aggression against Ukraine, she is also a Ukrainian lawmaker for the Batkivshchyna party of former prime minister Yulia Tymoshenko.

She was flown home on Poroshenko's jet and met at Kyiv's Borispil airport by members of her family and a large crowd of well wishers.

"I want to ask for forgiveness those parents whose children did not return from the anti-terrorist operation, and I am still alive," Savchenko told journalists just after landing. "I want to ask for forgiveness all mothers whose children are in captivity, and I am free."

Meanwhile, social media were awash with messages of congratulations on her release from Ukraine and abroad.

"Great news for which we had to work for a long time," tweeted German Foreign Minister Frank-Walter Steinmeier, whose country together with France have been trying to usher forward the Donbas peace efforts.

"Long awaited good news, that the EU celebrates together with her country," the European Commission's foreign policy chief Federica Mogherini added.

Poroshenko tweeted at 2.54pm Kyiv time that a plane with Savchenko landed in the capital. Almost simultameously, news agencies reported that two Russian servicemen captured in the Donbas, Yevgeny Yerofeyev and Alexander Alexandrov, who were sentenced by a Ukrainian court to 14 years in jail for terrorism in April, are now back in Russia.

Poroshenko promised to step up efforts aimed at the return of other Ukrainians who are being held by Russian authorities. "It's good that now Nadia will join this struggle," Poroshenko added. "These steps would be impossible without the Minsk agreements, which clearly stated Russia's commitment to release all hostages."

Later the same day, Poroshenko's administration published his special decree, which was dated by May 24, pardoning two Russian servicemen.

According to Russian presidential spokesman Dmitry Peskov, Savchenko was formally pardoned by Putin prior to her release and transport back to Ukraine from the southern Russian city of Rostov-on-Don. "Relatives of the murdered journalists requested that Vladimir Putin pardon Nadiya Savchenko as a humane gesture," TASS quoted Peskov as saying.

Observers say Savchenko's release will play positively for both countries, especially in the ongoing effort to find a political settlement about the situation in the breakaway territories of the Donbas region.

On May 24, Poroshenko's media office said in a statement that the leaders of Germany, France and Russia support deployment of an OSCE police mission in the Donbas. The statement followed Poroshenko's phone negotiations with Putin, German Chancellor Angela Merkel, and French President Francois Hollande.

Savchenko's release should provide impetus for complete implementation of Minsk peace agreements, US Secretary of State John Kerry said in a statement on May 25.

"Her release, after a long ordeal that included solitary confinement, is an important part of fulfilling Russia's commitments under the Minsk agreements and should now provide impetus for their complete implementation," the statement said.

But while Savchenko's return home will bring Poroshenko some credit in the short term, it can also backfire due to her association with the Ukrainian political opposition.

"The longer term question is whether Savchenko will want to have a domestic political profile," Nomura International strategist Tim Ash wrote in a note. "She was elected as a lawmaker under [opposition leader Yulia] Tymoshenko's ticket, and the latter's more populist party is currently topping the opinion polls. Poroshenko will need to play all this carefully."