The 31-year-old Indomitable Lion has opted to join the 2016/17 Turkish top flight runners-up after reaching the end of his contract with city rivals Galatasaray.
Chedjou, who has 50 international appearances for Cameroon and played at the 2010 and 2014 Fifa World Cups, moved to Turkey in 2013 from French club Lille.
The centre-back made 119 appearances and scored 12 goals for Galatasaray during a four-year stint that saw him win the league title in 2015.
He also won an unprecedented three straight Turkish FA Cup titles in 2014, 2015 and 2016 as well as three Turkish Super Cup in 2013, 2015 and 2016.
Istanbul Basaksehir shocked Turkish football by finishing second behind Besiktas in the league and emerging runners-up in the Cup final last week.
They will compete in the Uefa Champions League third qualifying round, whilst their more illustrious city rivals and Turkish football giants Fenerbahce and Galatasaray play in the second-tier Europa League.

Sean Mitchell, 46, inflicted four stab wounds on Stephen Dagg, 53, when he attacked him from behind at the St Mary's Vaults pub in Stamford, Lincolnshire.
Lincoln Crown Court heard there was a history of hostility between the men.
Mitchell, who was a publican at the nearby Melbourn pub, had previously banned Mr Dagg from his premises.
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The court heard Mr Dagg was drinking in the St Mary's Vaults pub on 12 June when Mitchell burst in to the pub and was heard to say: "Where's that queer."
Witnesses then described Mitchell, a father-of-three, attacking Mr Dagg from behind and inflicting four "karate chop" type blows to his neck and shoulder area.
The publican of St Mary's Vaults confirmed all of her knives were accounted for which meant Mitchell must have brought his steak knife with him.
Mr Dagg was then chased three or four times around the pub and hid behind the bar before he managed to escape outside.
He was later admitted to hospital in Peterborough where was he treated for four stab wounds.
Mitchell, who also had a supervisory role at the St Mary's Vaults pub, later said he had no memory of the attack and simply did not know why it had happened.
Mark Watson, mitigating, admitted Mitchell had brought the weapon with him, but had no recollection of what happened.
He added: "He had and has no idea about the complainant's sexuality. It was simply generic abuse."
Mitchell, of All Saints Street, Stamford, admitted a charge of wounding Mr Dagg with intent to cause him grievous bodily harm and having an offensive weapon.
Istanbul Basaksehir have announced the signing of Cameroon defender Aurelien Chedjou on a three-year deal.
[NEXT_CONCEPT]
A publican who repeatedly stabbed a man with a steak knife has been jailed for four years.