Centre-half Watts, 21, has agreed a deal until the summer of 2012, having made 11 appearances since joining the Imps on loan in October. He has impressed at the centre of an improving defence, and his signing is seen as something of a coup for The Imps.
"I am really pleased to have Adam on board and his move here is a significant coup," said Sutton.
Left-back Joe Anderson, 20, came through Fulham's youth academy and will join on a contract until the summer of 2011. He began his career as a youth player at Fulham before he was promoted to the reserve team and was loaned out to Woking during the second half of the 08/09 season.
Anderson made his first team debut for Fulham on 23 September 2009 in a 2–1 Cup defeat at Manchester City. He came on as a replacement for Zoltán Gera in extra time.
"Joe is someone who I have kept tabs on for a long time and he's vibrant, has a good engine and is what I want in a player." Said Sutton.