In a fusion reactor environment, the irradiation of neutrons and helium (He) plasma produces a great number of self-interstitial atoms and vacancies in tungsten (W), which inevitably interact with alloying solutes to form mixed self-interstitial atoms and substitutional solutes. The interactions of solutes with He atoms affect the behaviors of both, and ultimately cause the formation of solute precipitates and He bubbles; however, the micro-mechanisms of this are still mysterious. In this work, we perform systematic ab initio calculations to study the mutual influence of solutes and He atoms on their behaviors. It is found that most of the considered solutes bind tightly with the most stable dumbbells forming mixed or dumbbells. Solute-mixed dumbbells can act as trapping centers for He atoms. Mixed dumbbells bind very tightly with interstitial He atoms and all the binding energies are larger than 1.0 eV. Compared with the energy for the formation of a W Frenkel pair with the presence of He, the energies needed for the formation of most solute-mixed Frenkel pairs are decreased while titanium, zirconium, niobium, hafnium, and tantalum-mixed Frenkel pairs are exceptions. Similarly, substitutional solutes can also trap interstitial and substitutional He atoms, and solutes bind stronger with interstitial He followed by and solutes while it is the opposite for interactions of substitutional solutes with substitutional He atoms. The underlying reasons controlling the interactions of mixed dumbbells and substitutional solutes with interstitial and substitutional He atoms are analyzed.