Both midfielders, Griffith has joined from Doncaster while Taylor arrives from non-league Nuneaton Borough.
"It's an opportunity that I will jump at because I want to do the best I can," Griffith told BBC Radio Stoke.
"When I came here, I just got my head down and worked hard and I'm pleased the gaffer has taken me on," said Taylor, who had been on trial.
Griffith also has experience of non-league football, having spent the last two seasons on loan at Stafford Rangers and Halifax Town.
"Obviously I want to play league football," said Griffith.
"At the time I could have just stayed at Doncaster but wanted to get out and play.
"Now I want to play at a good level and do well for myself which will mean helping the team too."
BBC