Both were among a sweeping raft of reforms announced last month after a meeting of the ruling Communist Party that mapped out policy for the next decade.
Under the new policy, couples will be allowed to have two children if one of the parents is an only child. Previously, a couple could generally only have a second child if both parents were only children.
The plan was envisioned by the government about five years ago, with officials worried that the strict controls were undermining economic growth and contributing to a rapidly ageing population China had no hope of supporting financially.
The resolution, formally approved by China's largely rubber- stamp parliament on Saturday, will allow local legislatures to decide when to implement the policies, Xinhua said.
Parliament also approved the abolition of the "re-education through labour" system, in place since 1957, which allows police to sentence petty criminals to up to four years' confinement in labour camps without going through the courts.
Critics say the system undermines the rule of law and is often used against political activists and followers of Falun Gong, a banned spiritual group.