It comes from the Classical honorific verb 「[賜]{たま}ふ」, which means "to give (from one in a higher position to one in the lower)". The Modern counterpart is 「お[与]{あた}えになる」 or 「[下]{くだ}さる」. The 「ふ」 has become 「う」 over time as you probably know.
This verb can be used as an honorific subsidiary verb following another verb. The Modern counterparts are 「~~てくださる」、「お~~になる」, etc.
「[創]{つく}りたもうた」 = 「創る」 + 「たもうた」 = "to create" + "gracefully did so (as a subsidiary verb)"
This verb phrase is in the past tense (た at the end). Classical verbs are conjugated in the Classical way even when they appear in the Modern context for the authors' intended aesthetic reasons. It is not even possible to conjugate them in the Modern way. The pronunciation, however, is often changed to its modern way and, therefore, reflected in the kana. たまふた is Classical and たもうた is Modern.
Thus, 「 [神]{かみ}の創りたもうた[世界]{せかい}」 means "the world which God (gracefully) created (for us)".
In the entirely "modern" Japanese, the phrase is equivalent to 「神のお創りになられた世界」or 「神の創ってくださった世界」 in meaning. That is if anyone is interested in the modern translation within Japanese.