The leftist moved to sack his centrist arch-rival earlier this month after Andrej Babis came under heavy fire for alleged tax evasion.
The leftist Sobotka moved to sack his centrist arch-rival earlier this month after Babis came under heavy fire for alleged tax evasion and embarrassing leaked conversations.
The tycoon, who ranks as the second wealthiest Czech national, has denied doing anything illegal, but nonetheless agreed to leave amid mounting public pressure.
Sobotka rejected two other candidates proposed by Babis, before agreeing to Ivan Pilny, a 72-year-old tech expert and head of the parliamentary economic committee, to replace him as finance minister.
The crisis came as opinion polls showed Babis's ANO (Yes) political movement headed for victory in legislative elections set for later this year.
"I decided to agree to the ANO request and I'm prepared to ask the president to name Ivan Pilny as finance minister, following the removal of Andrej Babis," Sobotka told reporters in Prague.
Sobotka added that this "would bring to an end the dispute inside the coalition".
Pilny, who was elected to parliament in 2013, headed the Czech branch of Microsoft from 1992-98 and national operator Cesky Telecom from 2000-2001.
President Milos Zeman is expected to consider the switch after he returns from China on Thursday.
Describing Pilny as "experienced" and "independent", Babis insisted he was "definitely not a puppet", but many observers of Czech politics regard Babis as the only real decision-maker in the party.
ANO has so far led opinion polls with support reaching as high as 30 percent -- twice as much as Sobotka's CSSD Social Democrats -- but experts say that could change after the current crisis.
Experts in Prague also believe that the crisis was in part triggered by the CSSD as an early campaign move ahead of the October 20-21 election in the EU and NATO member state of more than 10 million people.
Sobotka has been in office since 2014, with the CSSD sharing power in a coalition government with ANO and the smaller centre-right KDU-CSL Christian Democrats.
Analyst Jiri Pehe told AFP on Wednesday that while the government appears set to last until October’s election, "relations between Sobotka and the ANO movement will remain very tense" during the months of campaigning to come.
Pehe also suggests the scandal surrounding Babis means that even if ANO wins the election, it is unlikely that any other party will want to form a coalition government allowing it to take power.
A Slovak-born self-made magnate, Babis became one of the EU state's most popular politicians virtually overnight by selling himself and the party he forged in 2012 as being tough on corruption, something voters perceive as pervasive in often murky Czech politics.
But the 62-year-old is now facing tough questions over his own business dealings.
Parliament asked Babis last week to explain how he raised the money to buy his sprawling Agrofert farming, chemicals and media conglomerate.
Questions have also come up about Babis's purchase of tax-free bonds issued by Agrofert, with critics insisting that as a finance minister fighting tax evasion, he should not benefit from tax loopholes.
Babis placed his Agrofert assets into a trust earlier this year to ward off conflict of interest allegations.
He is also under fire over leaked conversations revealing that he pressured a journalist from his media group to attack political rivals.
Babis admitted to "making an error" but insisted the leaks resulted from "a provocation orchestrated in advance".