Both groups will be entitled to broadcast campaign speeches, receive a publicly funded grant of up to £600,000 and send a leaflet to each household. A higher sending limit of £7m is imposed on the campaigns.
Britain Stronger in Europe was chosen by default after being the only pro-EU group to apply.
However, Vote Leave was vying with Grassroots Out, each of which mounted heavy campaigns in the build-up to the decision. The Trade Unionist and Socialist Coalition also applied, but their application "did not demonstrate that it adequately represented other campaigners".
Claire Bassett, chief executive of the Electoral Commission said: "Where there are competing applicants for a particular outcome the law is clear, we must designate the applicant which appears to us to represent those campaigning for that outcome to the greatest extent.
"We received two high quality applications on the "Leave" side, from "Vote Leave Ltd" and "The Go Movement Ltd".
"After careful consideration, the Commission decided that "Vote Leave Ltd" better demonstrated that it has the structures in place to ensure the views of other campaigners are represented in the delivery of its campaign. It therefore represents, to a greater extent than "Go Movement Ltd", those campaigning for the "Leave" outcome, which is the test we must apply.
"We encourage all campaigners to now focus on engaging voters on the historic decision they will have to take on 23 June," she added.
In addition to the benefits above lead campaign groups can have a dedicated page in the Commission’s public information booklet which will be distributed to all households in the UK.
In that booklet, there can also be the inclusion of a link to a page on the campaigner’s website, which should include their opinion on what will happen in the event of either referendum result.