B737 Captain reported a flight control malfunction during takeoff. The flight returned to the departure airport and landed safely.

Narrative

During rotation MASTER caution FLT CONT (Flight Control) Annunciated. Continued take-off/climb out. Flight controls responded normally; no secondary indications. Completed QRH which states to continue. Advised Dispatch and requested Maintenance Control be notified. Submitted ELB (Electronic Log Book) entry; reviewed MEL guidance. Concerned ZZZ station may not be able to comply with MEL requirements for the outbound flight; requested ARINC provide phone patch with Dispatcher. Discussed with Dispatch and advised to continue to ZZZ. At XA:37 received ACARS message OKAY COMPANY WOULD LIKE A RETURN TO THE FIELD DO TO THE MX (Maintenance) HANDLING OF THIS" for clarity we contacted Dispatch via ACARS IS REQUESTING AIRCRAFT X DIVERT TO ZZZ1. Upon receiving confirmation we notified ZZZ [ARTCC]; sent a diversion message via ACARS; and briefed the FA (Flight Attendant) and passengers. We were unable to contact ARINC via VHF until approximately XB:05 when we set up a second phone patch with Dispatch. Requested 1. Gate Info 2. Would crew and passengers be required or not required to process immigration and customs since the flight did not land. 3. Will the aircraft be replaced and if so what will be the new gate for the outbound flight. 4. Consult with the Crew Desk to determine crew legality for onward segments. This information was necessary to properly brief the passengers and keep them informed. During the decent Dispatch advised via ACARS Crew Scheduling was replacing the flight crew. Dual FMC failure after landing. Blocked in Gate XX but no gate agent to meet the flight. Terminated and debriefed Maintenance."