Final answer:
Rutherford B. Hayes became the President after the contested 1876 election, following a special commission awarding him the electoral votes despite Samuel Tilden winning the popular vote.
Step-by-step explanation:
The President who entered the White House after the fraudulent election of 1876 was Rutherford B. Hayes. In an election marked by controversy and disputed returns from several states, the Democratic candidate Samuel Tilden won the popular vote but fell short in the Electoral College.
A special election commission awarded the disputed electoral votes to Hayes, effectively granting him the presidency. This decision was part of the Compromise of 1877, which also resulted in the informal agreement to withdraw federal troops from Southern states, marking an end to Reconstruction.