Wales midfielder Tudur-Jones will sign a two-year contract at Easter Road when he leaves Inverness later this summer.
And McGivern, who enjoyed a successful loan period at Hibs last season, will sign a permanent deal once his Manchester City contract expires.
The news ends Tudur-Jones' two-year association with Caley Thistle, and he told the Hibs website: "The move 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."
Hibs will be in the Europa League qualifying rounds after finishing as Scottish Cup runners-up to Celtic.
And Tudur-Jones said: "I'm looking forward to playing in Europe. It's something a little bit different and it will be a great experience.
"Playing against different teams from different countries will be great for the continued development of the squad and it's something to get excited about."
Northern Ireland left-back McGivern 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."
Meanwhile, former Hibs striker Eoin Doyle has completed his move to Chesterfield after signing a two-year contract with the League Two side.