Madine has signed a two-year deal with Neil Lennon’s side after the expiry of his Hillsborough contract, while Amos has put pen to paper on a four-year deal after his impending transfer was confirmed in the middle of June.
A number of Championship clubs, including Birmingham, had been linked with Madine, who had been with Sheffield Wednesday since 2011.
The 24-year-old started his career with Carlisle and also returned to Brunton Park on loan, along with temporary stints with Coventry City and Blackpool.
Amos is no stranger to loan moves as well, having spent time with Bolton last season, when he made nine appearances after coming in at the end of January when first choice Adam Bogdan was injured.
He came through the ranks at Old Trafford, making his debut in 2008, but he would only go on to make six further appearances in the following seven years.
Other loan spells saw Amos spend time with Peterborough, Norwegian side Molde, Oldham, Hull City and Carlisle.
As well as the two new signings, midfielder Pratley has committed his future to the Macron Stadium side for a further three years.
Pratley has made a total of 117 appearances for Bolton since his arrival on a free transfer from Swansea in 2011.