The Reds also will get a player to be named or cash, according to sources.
In separate moves, the A's agreed to a $750,000, one-year contract with outfielder Gabe Gross and claimed infielder Steve Tolleson off waivers from Minnesota. They designated Taveras for assignment, along with left-hander Dana Eveland, to create space on their 40-man roster.
"I think we've been able to do some things to improve our club where we weren't too sure we would be in position to do that," Reds general manager Walt Jocketty said. "A lot of it was being patient and waiting for the market to drop to our level, where we could afford to do some things."
Miles, 33, was a disappointment with the Cubs last season, hitting .185 in 74 games -- and likewise, the 28-year-old Taveras struggled with the Reds, hitting just .240 in 102 games.
The $1.3 million the Reds save with this deal helps offset some of the money they just committed in signing shortstop Orlando Cabrera.
For Oakland, a primary motivation could be the addition of a useful utilityman who will be inexpensive.
The Athletics had tried and failed to sign Jamey Carroll earlier in this offseason for about seven times what Rosales, 26, will cost.
Known for his high energy, Rosales played all four infield positions in his two years with the Reds.
Taveras will make $4 million in the second season of a two-year deal, while Miles will be making $2.7 million this season in the second year of his two-year deal.
"He played an important role in that club in 2006 when [David] Eckstein got hurt late in season and we were without a shortstop," Jocketty said of Miles. "He played flawlessly at short. He's played all the positions except catcher and first base."
In addition to Gross' $750,000 base salary, he would get $25,000 each for 300 and 350 plate appearances and $50,000 apiece for 400, 450, 500 and 550 plate appearances.
Gross hit .227 with six homers and 36 RBIs in 115 games with Tampa Bay last season. He also has played for Toronto and Milwaukee.
Tolleson played at Double-A and Triple-A last season, batting a combined .266 with 27 doubles, eight home runs, 40 RBI and 13 stolen bases in 130 games.
Buster Olney is a senior writer for ESPN The Magazine. Information from The Associated Press was used in this report.