The children's charity has agreed a three-year contract worth £350,000 a year with Harrow Council to run the London borough's adoption service from 1 March.
Harrow has struggled to meet its targets for placing young people in adoption and was attracted by Coram's "excellent reputation".
"We have struggled with the recruitment of qualified staff, which isn't fair on the children," said Janet Mote, portfolio holder for children's services at Harrow.
A council spokeswoman added that the fee for the service was no more than the council already paid.
Jeanne Kaniuk, head of adoption and permanent families at Coram, said the takeover by charities of local authority adoption services could be the way forward. She said the fact that charities were generally smaller than local authorities meant they were more flexible.
Coram's 300 staff place about 70 children a year.