Blanche K Bruce and Hiram Rhodes Revels were able to become US Senators from Mississippi thanks to the era of Reconstruction.
Reconstruction was the time period after the Civil War. During this twelve year period, the US Congress passed several different amendments and laws to ensure that African-Americans had equal rights. One of the most significant laws was the 14th amendment. This stated that anyone born on American soil is considered a US citizen. This amendment also ensures that these citizens have the same protections/rights as all other citizens.
Since both of these men were born in the US and meet the requirements needed to become Senators (30 years old, must live in area that you are representing) they were allowed to become Senators.