The present mosaic, executed in 1878, is a fair copy of the destroyed late 13th century one, but not a stylistic replica. The original was executed in the year after 1291 by two Franciscan friars, Jacopo da Camerino and Jacopo Torriti, who were commissioned by Pope Nicholas IV who was himself a Franciscan. You can see their self-portraits among the Apostles below the main mosaic.

(Detailed description of the mosaic here)