Greybull Capital has bought the airline from the Mantegazza family which has owned it since the 1960s.
More than 90% of unionised staff voted to accept the changes. Two-thirds of the redundancies will be voluntary.
The fleet will be reduced from 42 aircraft to 34, and long-haul and charter flying will end by April.
The network will specialise in Monarch's scheduled short-haul European leisure routes.
Jim McAuslan, general secretary of the British Airline Pilots' Association, said: "Monarch's continuing presence in the marketplace is good for customers so this new investment is welcome."
He added it was "in no small part due to the painful sacrifices made by pilots and other staff, who have accepted redundancies and a substantial cut in pay and conditions to help secure jobs."
Speaking on behalf of the family, Fabio Mantegazza said: "We are very proud to have created one of the most loved aviation brands in the UK over the last 46 years.
"We think that now is an appropriate time to allow new shareholders to take Monarch into the future with secure financial backing and clear strategic goals."
Staff at Monarch airlines have agreed to 700 redundancies and pay cuts of up to 30% as part of a deal to save the Luton-based company.