I will praise thee, O Lord my God, with all my heart - This is but carrying out the idea in the previous verse. He would give his whole heart to God. He would allow nothing to divide or distract his affections. He would withhold nothing from God.
And I will glorify thy name for evermore - Not merely in the present emergency; but I will do it ever onward - even to eternity. The meaning is, that he would in all cases, and at all times - in this world and in the world to come - honor God. He would acknowledge no God but him, and he would honor him as God.