The move ends speculation that the 42-year-old - already interviewed as a potential successor to the departing Alan Gaffney at Munster - would be a prime target for the vacated Leinster hot seat.
Having taken over the Connacht coaching reins from Steph Nel in the summer of 2003, Bradley guided the men from the west to both the Celtic Cup and Parker Pen Challenge Cup semi-finals in his first season in charge.
This year, the Challenge Cup semi-finals have been reached again and Connacht are hoping to avenge a 25-18 first leg deficit in their second leg clash with Sale at Edgeley Park on Sunday, April 24.
Bradley - who also guided Ireland 'A' to success over their French counterparts last month - said: "I have great respect for the people here in Connacht, the players, management and supporters. They showed great loyalty through this process, understanding and supporting why I might be linked to the Munster job, while at the same time maybe hoping I would not go there.
"We have some interesting signings lined up - there is a bright future for Connacht rugby and I am looking forward to the challenge.
"There are various targets for us and Heineken Cup qualification is obviously one of them. It would be great if that were to happen," added Bradley.
Connacht CEO Gerry Kelly added: "While understanding why Munster would like to have Michael, I am delighted that he has decided to stay with Connacht. He has done tremendous work here over the past two years.
"There has been excellent growth and we need the trend to continue in the next few years," stated Kelly.