Council members are also proposing two charter amendments to help renters in Minneapolis.
The "Safety for All Budget Plan" was introduced Friday.
The new policy for Minneapolis Police Department was announced Wednesday.
The approval comes days after a tense exchange between the police chief and council members.
A committee narrowly passed the proposal that would allow the MPD to contract with other agencies to curb violence.
Council members say residents are asking "Where are the police" and are reporting officers say they need more resources to respond to crime.
The bill passed the House and Senate in the early hours of Tuesday.
Gov. Tim Walz has called a special session that starts Monday.
The City Council will next discuss the proposed changes Wednesday.
Lawmakers failed to agree on other critical legislation as well.
House leaders say the Senate's bills don't do enough to enact systemic change.
The plan will be put forward during the special session.
Gov. Walz wants to focus on police reform.
Democratic leaders announced Monday a bill that includes banning chokeholds and no-knock warrants