Both players were unlikely to get regular first team football this season and a move across the capital was in both players interest. Zamora has been handed a four-year-deal and Pantsil and three-year deal.
Zamora told Fulham's official site, "I am delighted that we have reached an agreement to enable me to play for Fulham next season.
"I am looking forward to joining the rest of the team this week and preparing for the new campaign.
"This is a new challenge for me and the prospect of working with a coach of Roy Hodgson's caliber was a great opportunity, so I am excited at the prospect of competing for a regular place in the team."