The Swede signed a two-year deal at the Midlands club on Saturday with the aim of taking them back to the English top flight for the first time since 2004.
The club were taken over in August by an Asian consortium led by Thai businessman Aiyawatt Raksriaksorn of the King Power Group, a duty free empire.
Asked at a news conference why he had joined Leicester, Eriksson replied: "Ambition of the club.
"I want to go and manage in the Premier League again, that's why I'm here," he added.
"Hopefully it will happen this year and if not this year then the year after... the money is there to support that idea."
He joins with the club in 22nd position in the 24-team league, having watched them beat Scunthorpe United 3-1 on Saturday to climb off the bottom of the table.
Eriksson takes over from Paulo Sousa who was sacked on Friday after the club won just one of their opening nine games of the season.
The Swede became the first foreigner to coach England in 2001, a position he held until 2006. He has also coached English clubs Manchester City and Notts County, while his most recent job was coaching Ivory Coast at the World Cup in South Africa.
His time at Notts County as director of football lasted six months and Eriksson said the finances that had been promised had never materialised. This time it would be different and he was also looking forward to getting back to a more hands-on job.
"This is a real project," he said. "That (Notts County) was not real and that was a pity. I don't want to sit in meetings all day."
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