In plants, chloride channels (CLC) are involved in a series of specific functions, such as regulation of nutrient transport and stress tolerance. Members of the wheat Triticum aestivum L. CLC (TaCLC) gene family have been proposed to encode anion channels/transporters that may be related to nitrogen transportation. To better understand their roles, TaCLC family was screened and 23 TaCLC gene sequences were identified using a Hidden Markov Model in conjunction with wheat genome database. Gene structure, chromosome location, conserved motif, and expression pattern of the resulting family members were then analyzed. Phylogenetic analysis showed that the TaCLC family can be divided into two subclasses (I and II) and seven clusters (-a, -c1, -c2, -e, -f1, -f2, and -g2). Using a wheat RNA-seq database, the expression pattern of TaCLC family members was determined to be an inducible expression type. In addition, seven genes from seven different clusters were selected for quantitative real-time PCR (qRT-PCR) analysis under low nitrogen stress or salt stress conditions, respectively. The results indicated that the gene expression levels of this family were up-regulated under low nitrogen stress and salt stress, except the genes of TaCLC-c2 cluster which were from subfamily -c. The yeast complementary experiments illustrated that TaCLC-a-6AS-1, TaCLC-c1-3AS, and TaCLC-e-3AL all had anion transport functions for NO3− or Cl−, and compensated the hypersensitivity of yeast GEF1 mutant strain YJR040w (Δgef1) in restoring anion-sensitive phenotype. This study establishes a theoretical foundation for further functional characterization of TaCLC genes and provides an initial reference for better understanding nitrate nitrogen transportation in wheat.