Northern Ireland left-back McGivern spent the last 12 months on loan at Easter Road but has now agreed a two-year deal with the Edinburgh club after City decided against renewing his contract.
And Tudur Jones is also heading for the capital after penning a two-year agreement.
The six-times capped Wales international helped Caley Thistle record their best-ever Clydesdale Bank Premier League finish of fourth this season but both he and McGivern can now look forward to Europa League football with the beaten William Hill Scottish Cup finalists.
McGivern, capped 19 times for his country, said: "I'm really pleased to have agreed to join Hibs on a permanent basis and I'm excited about what we can achieve as a group next season.
"There were other options available for me down south in England, but I wanted to stay with Hibs and continue my development at the club."
And Tudur Jones, who made 39 appearances for Inverness last term as they missed out on a European slot following a last-day Highland derby defeat to Ross County, added: "The move to Hibs is a fresh challenge and one I'm really excited about.
"Throughout my career, I've always chased new challenges and not wanted to stand still.
"Now I see Hibs as a challenge for myself - to help the club finish as high as possible in the table, which is where the club should be."
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- Tudur Jones