We develop a Bayesian multi-SNP Markov chain Monte Carlo approach that allows published functional significance scores to objectively inform single nucleotide polymorphism (SNP) prior effect sizes in expression quantitative trait locus (eQTL) studies. We developed the Normal Gamma prior to allow the inclusion of functional information. We partition SNPs into predefined functional groups and select prior distributions that fit the group-specific observed functional significance scores. We test our method on two simulated datasets and previously analysed human eQTL data containing validated causal SNPs. In our simulations the modified Normal Gamma always performs at least as well, and generally outperforms, the other methods considered. When analysing the human eQTL data, we placed all SNPs into their actual functional group. The ranks of the four validated causal SNPs analysed using the modified Normal Gamma increase dramatically compared to those of the other methods considered. Using our new method, three of the four validated SNPs are ranked in the top 1% of SNPs and the other is in the top 2%. For the standard Normal Gamma, the best of the other methods, the four validated SNPs had ranks in the top 1%, 4%, 20% and 59%. Crucially these substantive improvements in the ranks make it highly likely that most, if not all, of these validated SNPs would have been flagged for follow-up using our new method, whereas at least two of them would certainly not have been using the current approaches.