The 29 year-old Scotland international has been a long-term target of Ibrox boss Walter Smith and after making an initial offer of £750,000 in January, the clubs have now come to an agreement, according to various reports in the Scottish press.
The Glasgow Evening Times claims McCulloch will travel north on Wednesday for a medical and contract talks before joining his boyhood heroes on their pre-season tour of Germany on Thursday.
McCulloch joined Wigan from Motherwell in a £700,000 deal six years ago and established himself as a fans' favourite as Latics moved from the third tier of English football into the Premiership.
Berti Vogts handed him his first Scotland cap in 2004 and he has been a regular feature in the squad since, winning most of his caps during Smith's spell in charge of the national side.
The move will take Rangers' summer spending to around £5.2million after the captures of DaMarcus Beasley from PSV and Osasuna defender Carlos Cuellar.
Vi bruger cookies for at kunne give dig den bedste oplevelse. Ved at bruge vores side accepterer du brugen af cookies. Du kan læse mere i vores persondatapolitik.