The Exiles' maiden Premiership appearance against one of the powerhouses of the English game comes after a turbulent summer where they had been in danger of being denied promotion.
The Championship winners were originally denied the right to take their place in the top flight after the Rugby Football Union adjudged they did not meet the minimum standards required.
This was primarily because they did not have primacy of tenure at the Kassam Stadium, which they will share with Oxford United from this season.
But Welsh successfully argued that the primacy of tenure rule breached British and European competition law, and were finally granted Premiership status at the end of June.
But that left coach Lyn Jones with little time to pull together a squad ready to cope with the rigours of Premiership action. His most high-profile acquisition was that of Gavin Henson who will be out for over a month with a cheekbone fracture.
And with Leicester having appeared in the last eight Premiership finals and boasting a settled squad, the Tigers will start as overwhelming favourites to chalk up a comfortable win.
But Cockerill warned the battle Welsh have faced just to get to this stage makes them a dangerous opponent.
He said: "London Welsh fought hard to get into the Aviva Premiership and it will be a big occasion for them in their first Premiership game. There is a lot of experience in their squad and their coaching team.
"We've got to be accurate in what we do. We've got some good competition for places in the squad, we've given them all valuable game-time in the pre-season, but this is where it really matters."
Welsh, who have new signings Phil MacKenzie, Sonny Parker, Franck Montanella, Paulica Ion and Kirill Kulemin in their starting line-up, will hope they can emulate Exeter's recent successes.
The Chiefs were heavily fancied to be relegated when they were promoted two years ago, but retained their top-flight status with ease and ended last season qualifying for the Heineken Cup.
Welsh captain Jon Mills said: "It's a fantastic start to the season.
"We are looking to ruffle a few feathers this year and aren't there just to make up the numbers.
"Look at what Exeter have done since they have been promoted - that's the template we want to copy."
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