Transcription factors (TFs) are regulatory proteins that bind DNA in promoter regions of the genome and either promote or repress gene expression. Here, we predict analytically that enhanced homooligonucleotide sequence correlations, such as poly(dA:dT) and poly(dC:dG) tracts, statistically enhance nonspecific TF-DNA binding affinity. This prediction is generic and qualitatively independent of microscopic parameters of the model. We show that nonspecific TF binding affinity is universally controlled by the strength and symmetry of DNA sequence correlations. We perform correlation analysis of the yeast genome and show that DNA regions highly occupied by TFs exhibit stronger homooligonucleotide sequence correlations, and thus a higher propensity for nonspecific binding, than do poorly occupied regions. We suggest that this effect plays the role of an effective localization potential that enhances quasi-one-dimensional diffusion of TFs in the vicinity of DNA, speeding up the stochastic search process for specific TF binding sites. The effect is also predicted to impose an upper bound on the size of TF-DNA binding motifs.