The expansion is a result of the funding boost announced by the UK government last year.
The new languages will be Afaan Oromo, Amharic, Gujarati, Igbo, Korean, Marathi, Pidgin, Punjabi, Telugu, Tigrinya, and Yoruba.
The first new services are expected to launch in 2017.
Pidgin - West African lingua franca
Asian languages:
"This is a historic day for the BBC, as we announce the biggest expansion of the World Service since the 1940s," said BBC director general Tony Hall.
"The BBC World Service is a jewel in the crown - for the BBC and for Britain.
"As we move towards our centenary, my vision is of a confident, outward-looking BBC which brings the best of our independent, impartial journalism and world-class entertainment to half a billion people around the world.
"Today is a key step towards that aim."
The plans include the expansion of digital services to offer more mobile and video content and a greater social media presence.
On Wednesday the BBC launches a full digital service in Thai, following the success of a Facebook-only "pop-up" service launched in 2014.
Other expansion plans include:
£289m
investment
11
new languages
12 new or expanded daily TV and digital bulletins
40 languages covered after expansion
500m  people reached by 2022 - double the current number
1,300 new jobs, mostly non-UK
Fran Unsworth, the BBC's World Service director, said: "Through war, revolution and global change, people around the world have relied on the World Service for independent, trusted, impartial news.
"As an independent broadcaster, we remain as relevant as ever in the 21st Century, when in many places there is not more free expression, but less.
"Today's announcement is about transforming the World Service by investing for the future.
"We must follow our audience, who consume the news in changing ways; an increasing number of people are watching the World Service on TV, and many services are now digital-only.
"We will be able to speed up our digital transformation, especially for younger audiences, and we will continue to invest in video news bulletins.
"What will not change is our commitment to independent, impartial journalism."
The new language services mean the BBC World Service will be available in 40 languages, including English.
Lord Hall has set a target for the BBC to reach 500 million people worldwide by its centenary in 2022.
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The BBC World Service will launch 11 new language services as part of its biggest expansion "since the 1940s", the corporation has announced.