The double beta decay of ¹⁰⁰Mo to the 0⁺₁ and 2⁺₁ excited states of ¹⁰⁰Ru is studied using the NEMO 3 data. After the analysis of 8024 h of data the half-life for the two-neutrino double beta decay of ¹⁰⁰Mo to the excited 0⁺₁ state is measured to be T_1/2^(2ν) = [5.7^+1.3_−0.9 (stat.) ± 0.8 (syst.)]×10²⁰ y. The signal-to-background ratio is equal to 3. Information about energy and angular distributions of emitted electrons is also obtained. No evidence for neutrinoless double beta decay to the excited 0⁺₁ state has been found. The corresponding half-life limit is T_1/2^(0ν) (0⁺ → 0⁺₁) > 8.9 ×10²² y (at 90% C.L.). The search for the double beta decay to the 2⁺₁ excited state has allowed the determination of limits on the half-life for the two neutrino mode T_1/2^(2ν) (0⁺ → 2⁺₁) > 1.1 ×10²¹ y (at 90% C.L.) and for the neutrinoless T_1/2^(0ν) (0⁺ → 2⁺₁) > 1.6 ×10²³ y (at 90% C.L.).