Haymarket, which publishes Media Week, already owns Children Now and Young People Now.
Haymarket Professional publishing director Richard Watts said Nursery World would be a "great complementary fit" with the group's existing titles.
TSL, which used to owned by News International, said it had sold Nursery World because it wanted to focus on the school and university sectors, in which it publishes the Times Educational Supplement and the Times Higher Education Supplement.