Sudanese President Omar al-Bashir ordered the release of Jasek in order to maintain good relations between Sudan and Czech Republic, where Jasek is from.
Jasek was arrested along with three local men - including two pastors - after they raised money to help a man injured in a protest.
Sudanese authorities charged the group with espionage.
Rev Kuwa Shamal Abazmam Kurri was released in January 2017 after a judge found no evidence against him.
Church of Christ pastor Hassan Abduelraheem Kodi and student Abdulmonem Abdumawla were sentenced to 12 years behind bars.
At a press conference on Sunday, Sudanese Foreign Minister Ibrahim Ghandour said that Jasek would be handed over to his Czech counterpart Lubomir Zaoralek later in the day.
"Mr Jasek will accompany the Czech foreign minister to his homeland," Ghandour said.
Zaoralek later posted a video of him with Jasek on the flight home on Twitter.
Dnes máme za sebou dlouhý den, ale podařil se! Petr Jašek, který byl od roku 2015 zadržen v Súdánu, je doma. pic.twitter.com/Zb7UGBiMui— Lubomír Zaorálek (@ZaoralekL) February 27, 2017
According to the Prague Daily Monitor, more than 400,000 people had signed a petition for Jasek's release.
Speaking on Premier News Hour, Christian Solidarity Worldwide's Sudan Advocacy Officer - who we cannot name for security reasons - said Jasek's release was good news.
"After 14 months of being in prison, they've moved from one jail to another, standing trial, being accused of spying and very serious crimes which the whole group has maintained they have not committed, it's absolutely fantastic news," she said.
She added that CSW will continue to advocate for the release of the remaining prisoners.
"Logic would dictate they should also be freed – perhaps on similar grounds. The use of a presidential pardon is a discretionary power – it's not connected with a legal position as such so we are really in a position of just waiting and seeing."
"The other men are Sudanese nationals so aren't represented in the same way. It's important for us to continue raising the case with the diplomatic community to ensure they are also freed."
Listen to Aaron James speak to CSW here: