Branyan's deal also includes a possible $1 million in incentives for this year, and contains a $5 million mutual option for 2011. Branyan, 33, drove in 76 runs in 116 games for Seattle last season, and drew 58 walks.
The Indians were expected to try Matt LaPorta at first base, but there is concern that he may need more time to be groomed at the position.
Branyan presumably will have a shot at being the Indians' regular first baseman, and be part of what is expected to be a good offense.
Branyan began his career with the Indians in 1998, and over the last 12 seasons, he has appeared in 882 games, with 164 career homers.
There had been concern in some front offices about the condition of Branyan's back, which contributed to a second-half slump in 2009.
But Branyan has been working out at Vanderbilt in Nashville, Tenn., in recent weeks, and Tim Corbin, the baseball coach there, said several weeks ago that Branyan looked good, and was moving well.
Buster Olney is a senior writer for ESPN The Magazine.