Midfielder Keith Fahey will also be offered a new deal after an impressive season, less than 18 months after joining from St Patrick's Athletic.
Taylor's current deal expired this summer and the 38-year-old spent the last campaign as number two to on-loan Joe Hart who has now been replaced by £6million capture Ben Foster.
But the Northern Ireland international has impressed manager Alex McLeish sufficiently to be given a new contract.
McLeish said: "Maik has accepted a new deal. I can see him becoming a future coach.
"He is nearing the age of 40 but like David James he is in superb condition.
"I need Maik to drive Ben and he still has the hunger. I'm sure that he'll still be in Northern Ireland's thoughts which will keep him on his toes."
Regarding 27-year-old Fahey, McLeish said: "He has been instrumental in our success in the Championship, when we brought him in that January (2009), and this season in the Premier League, he's been a proven Premier League player.
"We will be discussing a new contract for Keith as well because he had an agreement that if he proved himself in the Premier League we would look at his wages.
"He came from St Patrick's on buttons. We improved it to kind of Championship money. Now he has proved himself to be a Premier League player."
McLeish is also confident his own new contract will be sorted out in the near future.
He said: "My advisers have contacted the club and I'm hoping that something can get done fairly quickly. I don't envisage any hold-ups. Hopefully we will get things tied up."