Three directors that represented Emirates Airlines, which is the second largest shareholder of the carrier, had also resigned last month.
SriLankan said U N B Obeysekera, Nihal Jayamanne, and Sanath Ukwatte has also been appointed directors.
The airline said Wikremasinghe was also the general manager of James Finlay Plantation Holdings Limited.
Wikremesinghe is the brother of first lady Shiranthi Rajapaksa.