The plan has received cross-party backing among city councillors – and town hall bosses will now draw up detailed proposals, saying it will help cut accidents.
The idea was proposed by the Liberal Democrats opposition and backed by the ruling Labour group.
It also called for a public information campaign on the 20mph zones, which are already in place outside many schools and some residential routes.
Victor Chamberlain, the Lib Dem councillor who put forward the motion, said: “Manchester has one of the worst records for road safety in the country. There are far too many needless deaths and while I support the fact the council has made steps to tackle this issue more still needs to be done.
“‘Twenty’s Plenty’ will have a significant impact on reducing the number of deaths and severity of accidents. It will also have a really positive impact on making roads more accessible, reducing pollution and encouraging people to walk and cycle.”
In 2010, 166 people were killed or seriously injured on Manchester’s roads.