The 27-year-old midfielder becomes Gary Naysmith s first permanent signing as Citizens boss.
Tapping spent last season at Stenhousemuir and was regarded as one of the best in his position in the league.
“Having worked with Callum previously, I know exactly what we are getting,” Naysmith told ECFC TV.
"He is an all round midfield player who can do a bit of everything. He was one of the best central midfielders in League Two last season and I am delighted that he has decided that his future lies with Edinburgh City.
"He has good experience of playing at a higher level and at 27, his best years are still in front of him."
Tapping, who spent time in Tottenham Hotspur’s academy, has previously been at Forfar Athletic, Brechin City and Queen of the South, where he was managed by Naysmith.
He made his breakthrough at Hearts, making 33 appearances across two years.
“Firstly a massive thanks to Stenhousemuir, a great club who will no doubt do well with ambitious people such as Jamie Swinney and Stephen swift leading the Club," Tapping said. “However I’m over the moon to sign with Edinburgh City.
"My decision was made after one conversation with the manager and James McDonaugh, they explained the direction the club wanted to go and I wanted to be part of it and most importantly the opportunity to work under the gaffer again alongside Grant Murray was a no brainer.
“I’m looking forward to meeting the squad now and to get going.”