The 31-year-old full-back was out of contract at the Rams this summer, having spent the last three seasons at Pride Park.
Elder, who spent time on loan at Town in 2019, now becomes the Imps' first signing since winning promotion to the second tier, after they lifted the League One title last season.
On moving to the LNER Stadium, the Australian said: "The football club has made fantastic progress over the past 12 months, both on and off the pitch, so it’s an exciting time to join Lincoln City and I’m really pleased to be here.
"I had some really good conversations with Chris Cohen and Tom Shaw. You could see their commitment to the project, their attention to detail, and their belief in what the club is trying to build.
"For them to believe that I am someone who can help to take the club forward is really exciting for me. I can’t wait to give everything I have to help achieve that."
Elder featured just five times for the Blues during his loan spell at Portman Road in the second half of 2018/19.