A total of 216 police officer jobs will be axed in Greater Manchester as the force attempts to save £14m from its budget for the next year.
Mr Todd has said he wants 11,000 officers in the force
The total number of GMP officers will fall to 7,849 as 74 divisional posts are cut and civilian staff replace officers on some desk duties.
Mounted and dog sections will also be centralised and funding withdrawn from initiatives to fight street crime.
Chief Constable Michael Todd says he wants to avoid compulsory redundancies.
Work has already started on freezing posts and negotiations are under way for those facing redeployment.
GMP said every effort would be made to protect frontline policing in the cuts, which were approved by the police authority at a meeting on Friday.
The force admitted changes such as centralising police dogs and horses would reduce the number of officers who could be deployed in response to incidents.
Mr Todd said he was confident his officers would continue to improve crime detection and reduction rates in the coming months, despite the cuts.
Last year Mr Todd described the force's budget settlement of £493.9m as "deeply disappointing".
On Friday, the police authority approved a budget of £503.5m for the 2006/07 financial year, 3.7% above its current level.
Chairman Derek Osbaldestin said the authority recognised the success of the force under Mr Todd but that members had to "take account of the economic pressures that all public sector organisations are under".
"This budget is a tough one, but we will continue to work closely with Mr Todd to identify and bring about savings whilst maintaining the momentum of continuous improvement that has been a feature of GMP's performance over the past few years," he said.
Although Mr Todd had previously said he wanted to see the number of GMP officers increased to 11,000, he recently warned that cuts were inevitable.
In a statement, Home Office Minister Hazel Blears said the government had done everything possible to maximise the increase in grant for all police authorities.
"There is simply no reason for Greater Manchester Police Authority to make cuts or set an excessive increase in its police precept on council tax that will put an extra burden on the local taxpayer," the Labour MP for Salford said.