He is the third IP minister since the post was created last July, but the first to be an elected member of parliament (MP).
The previous IP ministers, Lord Triesman and Baroness Morgan, were both members of the House of Lords.
The role includes oversight of the UK IP Office.
Lammy, 36, was formerly minister for skills in the same government department, the Department for Innovation, Universities and Skills (DIUS).
He is MP for Tottenham in London and studied law at the School of Oriental and African Studies before becoming a barrister. He was also the first black Briton to study for a Masters in Law at the Harvard Law School.
The previous IP minister, Baroness Morgan, has moved to the Department for Children, Schools and Families.
The new DIUS minister in the House of Lords, Lord Young, will have responsibility for skills and apprenticeships.
