The authority's planning committee earlier this month backed a ??35m proposal for the street's eastern side.
Campaigners condemned the decision, which will mean the demolition of the 103-year-old Futurist Cinema building.
The council said it was not possible to save the building or its facade due to its "poor structural condition" after many years of deterioration.
Liverpool Mayor Joe Anderson said the cinema was "close to my heart, as I know it is to many others" but two surveyors' reports had concluded "that there was simply no way it could be salvaged".
"There comes a point when you have to accept the inevitable and move forward and the government's decision allows us to do that," he added.
The national Cinema Theatre Association (CTA) earlier this week said the Futurist Cinema had "been allowed to rot away" for more than 35 years since its closure.
Steve Parry, managing director of Neptune Developments - the company behind the Lime Street plans - said the local Save the Futurist campaign group had "accepted that there is very little that can be saved".
"It's been frustrating to have London-based interest groups trying to derail the project," Mr Parry said, adding that his company had "demonstrated our commitment to conservation" with plans for an entertainment hub at the former ABC cinema.
He described the decision that the Communities and Local Government Secretary would not hold an inquiry was "a great result" as regeneration plans would have otherwise been "jeopardised" and "development stalled for up to two years".
A council spokesman said Lime Street's regeneration would include "radically redesigned buildings" and incorporate a hotel, shops, restaurants and student accommodation.
Mr Anderson added the plans would "bring Lime Street up to a much higher standard than it has been for decades".

Kerber, 28, beat Caroline Wozniacki in her semi-final as current number one Serena Williams lost against Karolina Pliskova to end 186 weeks at the top.
Germany's Kerber will officially become her country's first number one since Steffi Graf in 1996 when the new rankings are released next week.
"To be number one in the world sounds amazing," said second seed Kerber.
"For me it's amazing to be, after Steffi, the number one player from Germany," added Kerber, who is also the first German singles player to reach a US Open final since Graf in 1996.
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"Steffi is a great champion, a great person and I think she's proud of me to be the next number one after her."
In becoming number one, she also protects her compatriot's record of consecutive weeks at the top of the rankings as Williams' defeat to Pliskova of the Czech Republic leaves the American tied with Graf on 186 weeks.
Australian Open champion and Wimbledon runner-up Kerber, who won Olympic silver in Rio, will take on Pliskova in Saturday's final in New York, as she attempts to win a second Grand Slam title.
The government will not hold an inquiry into regeneration plans for Lime Street, Liverpool City Council said.
[NEXT_CONCEPT]
US Open finalist Angelique Kerber says that being able to call herself the new world number one "sounds amazing".