The two organisations began talks about a merger before Play Matters entered administration in February.
Their successful application to the transition fund, which the Office for Civil Society set up to help charities whose incomes have declined, enabled the merger to go ahead.
The Play Matters name, staff, contracts and assets have all transferred to the NCB. The charity awards grants and organises events to promote play among young children.
Nine staff members from Play Matters, including its chief executive Pauline Henniker, have joined the NCB.
But the future of seven members of staff depends on the renewal of service delivery contracts by two local authorities, the London Borough of Lewisham and Luton Borough Council. The contracts are due to expire in the current financial year.
The NCB’s 130 staff are unaffected by the move.
Michael Chuter, director of organisational support at the NCB, said: "Play Matters had realised that the business model they were operating under was going to be difficult in the new financial environment and they wanted a safe home.
"The NCB has a reputation for providing safe homes for a variety of organisations."