Coady, who spent last season on loan at Everton, will make a step down to the Championship with the Toffees beating the Foxes to survival.
He'll join in a £7.5million deal but the fee will rise to £8.5m if Leicester win promotion back to the Premier League.
The 30-year-old Liverpool native spent last season on loan at Everton after surprisingly leaving Wolves, who he previously captained.
Leicester are also set to complete the signing of goalkeeper Zack Steffen from Manchester City.
The American, who's been on City's books since 2019, spent last season on loan at Middlesbrough in the second tier.
Coady, meanwhile, helped the Toffees retain their spot in the Premier League ahead of Leicester, but he is now set to join them.
The ten-time capped England international would be the club's first signing under new manager Enzo Maresca, who left his role as Pep Guardiola's assistant coach at Manchester City to take over at the King Power Stadium.
Leicester have already seen Belgian international Youri Tielemans leave for free to join Aston Villa this summer, while in-demand midfielders James Maddison and Harvey Barnes are also set to depart.
Coady would be seen as an upgrade in defence, with the Foxes conceding 68 goals in 38 games last season under Brendan Rodgers and Dean Smith, the fourth-worst record in the league.
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Last summer, Leicester brought in centre-backs Wout Faes from Reims and Harry Souttar from Stoke, but failed to stop the rot at the back.
Smith even attempted to rush back Jonny Evans for the run-in, winning their final game of the season against West Ham, but they were still relegated.