In this paper, we introduce two new types of labelings of graphs using Fibonacci numbers namely, Fibonacci graceful labelings and Super Fibonacci graceful labelings. We discuss the existence and non-existence of Fibonacci and Super Fibonacci graceful labelings for certain classes of graphs. Also we discuss the Fibonacci gracefulness of disjoint union of Super Fibonacci graceful graphs, pendant edge extension of Super Fibonacci graceful graphs and amalgamation of Super Fibonacci graceful graphs. Finally, we compare the graceful graphs with Fibonacci graceful graphs.