We introduce a novel method for automatic detection of Atrial Fibrillation (AF) using time-varying coherence functions (TVCF) and Shannon Entropy (SE). The TVCF is estimated by the multiplication of two time-varying transfer functions (TVTFs). Two TVTFs are obtained using two adjacent data segments with one data segment as the input signal and the other data segment as the output to produce the first TVTF; the second TVTF is produced by reversing the input and output signals. The detection algorithm was tested on RR interval time series derived from two databases: the MIT-BIH Atrial Fibrillation (AF) and the MIT-BIH normal sinus rhythm (NSR). The MIT-BIH database contains a variety of short and long AF beats from 25 subjects and the MIT-BIH NSR database consists of only normal sinus rhythms from 18 subjects. Using the receiver operating characteristic curves from the combination of TVCF and SE, we obtained the accuracy of 97.49%, sensitivity of 97.41% and specificity of 97.54% for the MIT-BIH AF database. Furthermore, the specificity of the MIT-BIH NSR database was 100%.