"Thank God, the crew is alive", Russian President Vladimir Putin's spokesman Dmitry Peskov told reporters when it became clear that the crew had landed safely.
The rocket was carrying United States astronaut Nick Hague and Russian cosmonaut Alexei Ovchinin.
NASA said American astronaut Nick Hague and Roscosmos' Alexei Ovchinin lifted off as scheduled at 2:40 pm local time from the Russia-leased Baikonur cosmodrome in Kazakhstan atop a Soyuz booster rocket.
The Kremlin confirmed the men had survived.
Hague and Ovchinin will open the hatch to their spacecraft at 12:45 p.m. EDT (1645 GMT), when they will be greeted by their three Expedition 57 crewmates: NASA astronaut Serena M. Auñón-Chancellor, European Space Agency astronaut Alexander Gerst and Russian cosmonaut Sergey Prokopyev.
After the malfunction they were forced to return to Earth in a process known as a "ballistic re-entry", during which they experienced forces of up to 7G.
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The rocket was carrying USA astronaut Nick Hague and Russian cosmonaut Alexei Ovchinin.
In 2015, he was selected to participate in a space food taste test, sampling some 160 dishes designed for astronauts and cosmonauts on board the International Space Station.
Search and rescue teams were scrambled to the touchdown location as NASA revealed the descent meant the Russian-built Soyuz MS-10 spacecraft had to take "a sharper angle of landing compared to normal".
Search and rescue teams were heading to the area to recover the crew.
It was the first space mission for Hague, who joined NASA's astronaut corps in 2013.