Matthews, who suffered a crash in training that required six stitches in his hand, was not able to recover from the wounds sufficiently to start.
Meier flew from Vancouver to Leeds yesterday to join the team for his debut Tour de France.
"It hasn't really sunk in yet, it has been a little bit of a whirlwind 24 hours," Meier said. "It not the way you want to start a Tour just because a guy is injured, but I have to say, as my first Tour I am extremely excited to start.
"It's every bike riders dream to do the Tour de France one day and it's unbelievable that it is happening."
Matthews moved into the pink leader's jersey in the Giro d'Italia when the race was in Belfast in May, and won a stage while wearing that maglia rosa in Montecassino. He was expected to contend for stage wins in the Tour de France.
"Bling (Matthews) is an incredibly talented bike rider as he has shown," Meier said.
"He is one of those guys who is going to have a long and prosperous career ahead of him so emotionally it is pretty difficult not to start your first Tour but during his career he will have plenty more opportunities to do more Tours and win stages."