Cheika, pronounced with a silent 'i', has signed a three-year contract with the province and previously coached Italian side Padova and Randwick of Sydney, Australia, to Premiership glory in 2003/04.
The 38-year-old former back row said: "This is a fantastic opportunity to come to Leinster at this stage in my career. The class level of player is high here and to implement the type of game plan that I will look to introduce, you need top quality players.
"I'm looking forward to competing again in the Heineken Cup. I have some experience of what to expect from my time in Italy. It is important that we are successful in the Celtic League and it's important to combine both competitions so that we can strive for consistency."
The 41-year-old Knox, capped 13 times for Australia and a member of their 1991 World Cup-winning squad, is also of Randwick stock.
Knox admitted: "I was brought up watching exciting open rugby and I'm looking forward to working with what is an extremely talented group of players. We'll be looking to play a 15-man game and with four British and Irish Lions in the backline - including the captain - it's a squad that excites me.
"It wasn't a difficult decision to move here. I always wanted to live in Dublin having played here before and I'm looking forward to this opportunity."
Leinster Chief Executive Mick Dawson added: 'I am delighted to welcome both Michael and David to Leinster. They are one of the most exciting coaching partnerships in Australian rugby and we're delighted to have secured their services. I would like to take this opportunity to wish them well with the province."
Cheika is Leinster's third Australian coach since 2000, following in the footsteps of Matt Williams (2000-2003) and Gary Ella (2004).