BREAKING NEWS: Peterborough United pair join Imps
Bostwick has signed a two-year contract at Sincil Bank, while Anderson has committed to a three-year deal.
The combined fee will remain undisclosed.
Bostwick dropping down a division will come as a huge surprise to Posh fans.
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Hide AdLincoln have cash to burn after their FA Cup and promotion exploits last season.
Bostwick (29), who was placed on the transfer list in line with club policy after entering the last year of his contract. made 228 appearances for Posh following a reported £800,000 transfer from Stevenage in 2012. He scored 23 goals.
Anderson spent two spells on loan at Lincoln last season, helping them to promotion from the National League.
The 20 year-old only made 18 appearances for Posh. He joined the Posh youth academy from Crawley four years ago.
Posh play at Lincoln in a friendly on Saturday (July 22).