The skipper, who was signed up by Delhi for 11 million rupees ($133,000) in the player auction, has captained Australia in 100 of her 132 T20 international matches - the most by any woman in the game's shortest format.
Among the game's greats, she has scored more than 3,000 runs in T20 cricket with two hundreds and 15 fifties. She also has 15 hundreds and 21 half-centuries in the 50-overs format.
"It's a very proud moment for me, firstly to be involved with Delhi and then to lead them. It's about enjoying yourself, getting the best out of yourself," Lanning said.
"WPL is a massive moment for the sport, it's the logical next step and makes a lot of sense.
"Cricket in India is people's lives and the fact that WPL is up and running, and to be involved in something like this, is amazing. It's only going to grow in the coming years."
A five-times T20 World Cup winner, Lanning will have India's Jemimah Rodrigues as her deputy. Delhi begin their campaign against Royal Challengers Bangalore on Sunday.
Other Australians captaining their sides in the WPL include Beth Mooney (Gujarat Giants) and Alyssa Healy (UP Warriorz).
Indian captain Harmanpreet Kaur will lead Mumbai Indians and Smriti Mandhana will skipper Royal Challengers Bangalore.
Three of five the WPL teams are owned by Indian Premier League sides. The tournament will be played between March 4 and 26 at two venues in and around Mumbai.
