The noncoding genome is pervasively transcribed. Noncoding RNAs (ncRNAs) generated from enhancers have been proposed as a general facet of enhancer function and some have been shown to be required for enhancer activity. Here we examine the transcription-factor-(TF)-dependence of ncRNA expression to define enhancers and enhancer-associated ncRNAs that are involved in a TF-dependent regulatory network. TBX5, a cardiac TF, regulates a network of cardiac channel genes to maintain cardiac rhythm. We deep sequenced wildtype and Tbx5-mutant mouse atria, identifying ~2600 novel Tbx5-dependent ncRNAs. Tbx5-dependent ncRNAs were enriched for tissue-specific marks of active enhancers genome-wide. Tbx5-dependent ncRNAs emanated from regions that are enriched for TBX5-binding and that demonstrated Tbx5-dependent enhancer activity. Tbx5-dependent ncRNA transcription provided a quantitative metric of Tbx5-dependent enhancer activity, correlating with target gene expression. We identified RACER, a novel Tbx5-dependent long noncoding RNA (lncRNA) required for the expression of the calcium-handling gene Ryr2. We illustrate that TF-dependent enhancer transcription can illuminate components of TF-dependent gene regulatory networks.