Blues head coach Young had been linked with a move to the English giants for the second time this season after South African Meyer left the Tigers last month.
But the Arms Park chief has ended any lingering doubts over his immediate future.
Young declared: "I can categorically say that my future is here and I've got no interest in moving from the Blues.
"I'm 100 per cent committed to my chairman (Peter Thomas) here and to give the region and the supporters the success it fully deserves.
"I can't help the speculation or being linked with other clubs. Hopefully, this is the end of the matter and my future can be put to bed."
Young's stock has risen after guiding the Blues to their second successive Heineken Cup quarter-final and an EDF Energy Cup semi-final with Northampton Saints next month.
While Young will remain with the Blues, Jamie Robinson is set to seal a move to France with Toulon.
Robinson's contract expires at the end of the season and the 28-year-old is expected to pen a two-year deal.
And the Wales centre showed the capital region what they will be missing with a brace of tries in the 34-30 victory over Glasgow Warriors at the weekend.
Young said: "We want to keep all our best players and Jamie is one of those. But it's a two-way street and the player may decide where their future lies best.
"The French are flooding the market with a lot of money and that turns a lot of players heads. But we hope it doesn't come too thick and fast because we don't want to see an exodus of players from Wales."
Tom James and Dafydd Hewitt also touched down in an open contest against Glasgow as the Blues moved above Newport Gwent Dragons in the Magners League table.
Young said: "We've got a bonus-point and normally we'd be happy but the dressing room is disappointed.
"We were messy and didn't reach the levels we expect. We made too many mistakes, gifted them 14 points straight after half-time and let them back in the game. At times, we didn't quite click."