The forward, 30, joined the big-spending Lancashire side on Wednesday, and according to local media turned down the Iron and fellow League One side Coventry.
"We worked really hard to get Jon because a lot of other clubs were after him and he wasn’t spoiled for choice when it came to deciding where he wanted to move," said Cod Army manager Micky Mellon.
“He is the type of big target man, 6ft 4in, that we haven’t had at the club before, though that doesn’t mean that we will change the way we play - we will continue to try and play football.
“He will be the type of physical presence in the final third that we haven’t had. He is not just a big presence, but he is a good footballer as well.
“It is a massive statement that the club has made, and like all the other players we have signed they want to be a part of a team that is successful and moving upwards.”
Parkin was a free agent, after agreeing to leave Championship side Cardiff City last week despite having 12 months left on his contract.
He made 14 League One appearances on loan for the Iron last season, scoring six goals as he helped them avoid relegation to League Two. He made just 15 appearances in 18 months at Cardiff, netting twice.