The 30-year-old was released by Notts County having completed last season on loan at Cheltenham, starting their League Two final defeat to Crewe last weekend.
The well-travelled former Stockport, Hull and Blackpool forward has scored 86 goals in 361 professional appearances.
Rovers manager Ronnie Moore said: "I'm delighted that Ben will be signing for us. We beat off several clubs to secure his signature. He's big and strong and has an impressive strike rate for a target man.
"He'll lead the line for us, he'll cause defenders problems and he'll create chances for others. I watched him a few times for Cheltenham and Notts County at the end of the season and he did really well.
"Ben is the first of many new faces we'll have this summer and hopefully we'll have some more over the next few days and weeks."
