SAN FRANCISCO — Ahmad Brooks always wanted to stay in the Bay Area, a place that has become a new home after all those painful memories of getting cut by Cincinnati four years ago, and the San Francisco 49ers sure made it hard for him to leave.

Now the two are tied together long term.

Brooks signed a six-year, $44.5 million contract extension with San Francisco on Tuesday that will take him through the 2017 season and keep one of the NFL’s best linebacker units intact. The deal is worth $17.5 million guaranteed, said his agent, Greg Williams.

“Something was telling me just to sign here. I feel like this is where I should be,” said Brooks, who could’ve opted for free agency. “These are the people who gave me a chance to get this contract.”

Brooks emerged as a regular starter for the first time in his six-year NFL career last season.

Along with All-Pro inside linebackers Patrick Willis and NaVorro Bowman and sensational rookie Aldon Smith at the other outside spot, Brooks helped the 49ers win the NFC West behind one of the league’s best defenses. San Francisco allowed only 14.3 points per game, second only to Pittsburgh at 14.2.

The 49ers lost at home in overtime of the NFC championship game to the eventual Super Bowl champion New York Giants.