Wesley Thomas and Harlee Dean have been transfer-listed, while Mark Nwokeji, Alex Bentley and Hakeem Araba will not have their contracts extended.
However, goalkeepers Tony Roberts and Chris Lewington have both signed extensions to their deals.
Roberts, 40, has agreed a one-year deal with the option of another 12 months while Lewington, 21, has signed-up for two years.
I would hope we can retain most of our side now and give them a better wage, but surely some of our boys may struggle next season
arnu69
The signings of Lewis and Gwillim are the first by manager John Still since the Daggers claimed their historic League Two play-off victory at Wembley on Sunday.
Still had already brought in winger Danny Green and striker Alex Osborne before the end of the season.
Midfielder Lewis made 51 appearances for the Gills after signing from Stevenage Borough in 2008.
The former Spurs reserve player was part of the Kent club's League Two play-off winning side a season later.
Former Crystal Palace youth team player Gwillim played 121 games in the Blue Square Premier for Histon, after joining them from Bishop Stortford in 2007.
Despite still having a contract at the Glass World he was released by mutual consent.
Source: BBC Sport
Source: BBC Sport