The Buffalo Bills figure to consummate the second half of their Cincinnati daily double early this week when, as conventional wisdom now holds, the Bengals will not match the offer sheet signed by linebacker Takeo Spikes.

The first half of the equation, however, is completed.

After two weeks of deliberation former Bengals head coach Dick LeBeau, who was fired after three seasons, has agreed to join the Bills' staff as an assistant. The move has been rumored for weeks but LeBeau wanted to think about it before accepting the standing offer from head coach Gregg Williams and general manager Tom Donahoe.

Donahoe had noted at last month's NFL combine that he believed LeBeau, who begins work Monday, would join the Bills.

"My heart told me that I wanted to keep coaching," LeBeau said, "but I just wanted to make sure my head said the same thing. So I took a little while to sit back and really think hard about it. And I concluded this is something I really wanted to do."

A longtime coordinator, the 65-year-old LeBeau was 12-33 in his two-plus seasons as Bengals head coach. First as a coordinator and then as head coach, he tutored Spikes, who signed a six-year, $32 million offer sheet with the Bills as a "transition" free agent.

Cincinnati has a week to match the offer but, given that the Bengals reacted immediately to the move by signing linebacker Kevin Hardy and defensive tackle John Thornton on Friday night, the matter is considered academic. The Bengals could announce as early as Monday that they are not matching the offer sheet, thus permitting Spikes to join the Bills, where his presence would continue the overhauling of their linebacker corps.

LeBeau will be entering his 45th consecutive season in the NFL as a player or coach. Long noted as one of the game's best defensive minds, he is generally credited as having developed the zone-blitz scheme that pervaded the league in the 1990s and which remains a part of virtually every team's defensive playbook.

He will work primarily with Buffalo's secondary, likely fine-tune the Bills' use of some zone-blitz techniques, and also aid the offensive staff when the Bills face a defense that uses the zone-blitz package.

Defensive coordinator Jerry Gray will continue to call the schemes but LeBeau is likely to be involved in helping develop game plans. He becomes the third former head coach on Williams' staff, joining offensive coordinator Kevin Gilbride and running backs aide Les Steckel.

Even before he offered LeBeau a job, Donahoe was careful to consult with Williams and Gray about adding LeBeau. At the combine, Williams said he would be "thrilled" to have LeBeau come to Buffalo and that he did not mind the possibility of adding yet another former NFL head coach to his staff.

Len Pasquarelli is a senior writer for ESPN.com.