Eder, who previously had spells in the top tier of Portugal, Greece and Cyprus, joined Chennaiyin last year on a free transfer but his campaign was hampered by injuries and he could only make two substitute appearances.
The 32-year-old from Sao Paolo joined I-League outfit Salgaocar after ISL and made 12 appearances. He re-joins Chennaiyin on a free transfer.
Former I-League winner Pawan was signed by Chennaiyin on loan from I-League's Mumbai FC to replace injured custodian Nidhinlal midway through the 2015 ISL season and the 26-year-old Punjab player went on to be a part of the ISL winning squad.
Pawan made 11 appearances for Mumbai in the I-League and has now signed for Chennaiyin on a permanent deal.
"Although Eder did not get to play much last year he had a positive influence in the dressing room and we hope to have him at his best this year. Pawan is a great lad and team player. We are happy to have him back," said Chennaiyin FC coach Marco Materazzi.
"I would like to thank the owners and coach Marco Materazzi for giving me another opportunity at Chennaiyin. The club and the fans were fantastic towards me even though I hardly played due to injuries. I am determined to prove myself and help the team win the trophy again," said Eder.
"After not being included in the draft last year I thought I would miss out from playing in the ISL but Chennaiyin showed faith in me and I am grateful to them for believing in me this year again. I know it will very difficult to break into the first 11 but I will work very hard and keep myself ready whenever the coach would need me," Pawan stated.