The 615,429 sq ft City Tower, which is multi-let to more than 70 tenants, is part of the mixed-use Piccadilly Gardens-based scheme.
OBI will work with existing tenants and market the remaining office space within City Tower.
Current tenants at the building include The Ministry of Justice, Hays Recruitment and Starbucks.
The tower is owned as part of a joint venture between Schroder UK Real Estate Fund and Immobilien Europa Direkt.
“A number of tenants have signed new contracts at City Tower and we look forward to working with OBI on progressing the wider building strategy and leasing the remaining vacant space,” said Ross Cosslett, deputy fund manager of Schroder UK Real Estate Fund.
Will Lewis, co-founder of OBI, added; “ City Tower offers exceptional accommodation to potential occupiers which has very much been reflected through recent lease renewals and lengthened commitment by current occupiers.”