Anies, a former Jakarta governor, said the aim of the case was to ensure democracy was improved and said there were many problems with the election that needed to be corrected.
Anies declined to concede after the results were released on Wednesday and his team has alleged the current administration had unfairly sought to influence the contest, which authorities have rejected.
Official results showed ex-special forces commander Prabowo Subianto, who was tacitly backed by the hugely popular incumbent President Joko Widodo, won with almost 60% of the vote, followed by Anies with 25%, and former Central Java governor Ganjar Pranowo with 16%.
"The process and result are both as important. When there is a problematic process, there will be problematic results." Anies told a press conference.
"From the policy aspect, regulations, down to the execution (of the election) there were many problems and we want those corrected so they are not repeated."
The Anies team has complained about the widespread allocation of social assistance, such as rice, fertiliser and cash handouts, in key electoral areas, which they said influenced the vote. The administration has rejected that.
They have also criticised the Constitutional Court's last-minute decision last year to change election rules, which allowed the president's son to become Prabowo's running mate.
The court's chief justice at the time was Widodo's brother-in-law.
The judge was reprimanded by an ethics panel for intentionally allowing "intervention from an external party", which it did not name, but he was allowed to keep his seat on the bench.
Allies of the president, better known as Jokowi, have rejected allegations he interfered in the court's decision.
Both losing camps have alleged the electoral process was marred by widespread counting irregularities, with the Ganjar Pranowo team also expected to lodge a legal challenge. According to rules, a case must be lodged within three days of the announcement of the results.
Prabowo, a fiery ex-commander turned Tik Tok sensation swept to victory with the help of young voters and his promise of continuity.
Responding the results on Wednesday, Prabowo thanked his supporters, including Jokowi, and pledged to be a leader for all Indonesians. His team has said it has more than 30 lawyers ready to face any legal challenges.
