City had offered fresh terms to the versatile attacker, 25, who impressed under Mark Hughes's watch last term, but the lure of returning to his Lincolnshire roots and to a side in a higher division proved too strong.
Vernam said: “Being from the area it means a little bit more, my family live here and I’m incredibly proud to represent this club. I’m hoping to play a big role in this club on and off the pitch in the community.
“I’ve played against Lincoln for numerous clubs before and feel there is a very particular style I can fit into. It’s an opportunity to progress and make that step to the division above - every player wants to play at the highest level and it’s an opportunity to give the club everything as I come into the prime of my career.”
City head coach Mark Kennedy added: “He’s a Lincoln lad who we know is looking forward to representing his hometown club. He has excellent attributes, can create and score goals, will be a real attacking threat and we are delighted to have signed him when as a free agent, he’s had a lot of other interest. Charles is a great age and has the ability to make a big contribution in what we are building moving forward.”