Mr Babis, 63, is the country’s second-richest man and campaigned on an anti-establishment and Eurosceptic platform.
With all votes counted, his centrist movement ANO (Yes) collected a share of almost 30% – nearly three times that of its closest rival.
The centre-right Civic Democrats and the Pirates Party came second and third with more than 10% each.
The Pirates will make their debut in parliament with 22 seats, the news agency AFP reported.
Turnout was almost 61%.
Mr Babis is now set to become prime minister after coalition negotiations. However, he told news agency Reuters that while he had “invited everyone for talks”, he was not prepared to “cooperate” with either the far-right, anti-EU Freedom and Direct Democracy party or the Communist Party.
The 63-year-old made his estimated $4bn (£3bn) fortune in chemicals, food and media – but he has also faced numerous scandals including a fraud indictment and accusations he was a communist-era police agent.
He says he would not bring the Czech Republic in to the eurozone but he wants the country to stay in the EU, telling Reuters he would propose changes to the European Council on issues like food quality and a “solution to migration”.
The ANO’s current coalition partner, the ruling centre-left Social Democrats (CSSD), saw its share of the vote tumble to become the sixth-largest party, and has talked down the possibility of another coalition.
The Civic Democrats have also ruled themselves out of governing alongside Mr Babis.
Far-right and far-left groups made gains in the election. The largest parties now include:
The BBC’s correspondent in Prague, Rob Cameron, said the SPD’s performance was particularly noteworthy, as the far-right party wants to ban Islam in the Czech Republic. Its leader has urged Czechs to walk pigs near mosques.
Liberal, pro-European parties were left massively depleted, he said.
He sees the hand of this shadowy deep state everywhere; the media, the Czech prosecutor’s office, the Slovak Constitutional Court, even the EU’s anti-fraud unit. A host of enemies ranged against him in a vast anti-Babis conspiracy.
Well, if there was such a conspiracy, it’s failed.
His message to voters – that he alone could heal the ills of the Czech political and economic system, that he alone could decapitate the hydra of corruption, that he alone could defend Czech national interests – appears to have been heard. They have given him a convincing mandate. He has truly crushed his rivals.
He still needs friends – 78 seats is far from enough in a 200-seat lower house to do much of anything, let alone the sweeping constitutional changes he dreams of.
With eight other parties in parliament – from centre-left to far-right – he has a bewildering choice of coalition partners. It’s a choice that will determine the future course of the country.
But in May, Mr Sobotka submitted his government’s resignation because of a disagreement with Mr Babis, who was serving as finance minister at the time.
He was unhappy about alleged unexplained business dealings involving Mr Babis.
On seeing the rise of the SPD Mr Sobotka was shocked, saying; “How is it possible that in the Czech Republic, in a situation when the country is doing very well, when we are a stable, safe country, we have achieved many things in the social sphere in the past four years, people are increasingly in favour of extreme views?”
The Social Democrats’ tally of 7.3% was their worst result since the Czech Republic split from Slovakia in 1993.
“I`m glad you did not believe that, that you gave us the confidence to get a chance to form a government,” he said.