Adidas-Saloman immediately hailed the decision, which gives a green light for the transaction nearly six months after it was first announced last August.
"We are excited to have reached this important milestone," said adidas-Salomon chief Herbert Hainer. "We now expect that the transaction will close shortly, following approval of Reeboks shareholders."
The merger, which will create the world's second biggest sports clothing group after Nike, had already been approved by US competition watchdogs. But it still needed the approval of the European Union's executive arm.
"The investigation showed that there are horizontal overlaps between the activities of Adidas and Reebok," it said, but added that the two companies have "slightly different brand and pricing positions.
"Adidas is perceived as a professional, technically oriented brand with strong European roots," according to the commission. "Reebok predominantly targets young people and women, is more a leisure brand and has a stronger presence in American sports that are not excessively popular in Europe."
"Competition not significantly impacted"
The commission therefore "concluded that the transaction would not significantly impede effective competition in the EEA (European Economic Area) or any substantial part of it."
Adidas-Salomon and Reebok agreed the takeover last August. Adidas received the green light from the US competition authorities in October to take over its rival.
"To help ensure we hit the ground running on day one, our two companies have jointly developed an integration plan that leverages the talents and expertise of both companies," said the Adidas chief.