Lankesh will share the annual award, instituted in memory of a Russian investigative reporter who was assassinated last year in Moscow, with Pakistani activist Gulalai Ismail.
Ismail is fighting rightwing extremism in Pakistan.
The award is conferred by London-based organisation RAW in WAR (Reach All Women in War), and the announcement about Lankesh winning it was made to the media in Bengaluru by her mother Indira, brother Indrajit and sister Kavitha Lankesh.
"Anna was an activist-journalist just like my sister. She was killed on October 7, 2006, when she was in a lift. Five people accosted her and poisoned her," she said, quoting from the email.
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She was killed for speaking up against the human rights violations in then-restive Chechnya province of Russia and exposing corruption.
"In her name, the award has been instituted exclusively for women, to honour those who work towards upholding the human dignity, especially of women and children," she said.
Whether he was satisfied with the investigation by the 21-member Special Investigation Team formed by the Karnataka government, he said they wait for the killers to be caught.
"We can't say we are happy with the investigation till the killers are found. But we are satisfied with the work they are doing," Kavitha said.
She expressed unhappinessover speculative stories appearing in the media.
On October 3 this year, Karnataka minister Ramalinga Reddy claimed the SIT has identified the killers. He, however, did not share the details, saying the SIT was gathering more evidence.
Her assassination came days after the second anniversary of the killing of Kannada writer and rationalist M M Kalburgi, who fell to bullets fired by two unidentified men at his residence at Dharwad in north Karnataka in August 2015.