Found in the Preamble and in Article I, Section 8. This is one of the so-called “elastic clauses” that have been used to justify massive expansion of the federal government over the years. The original intent of the language is that any spending or legislation should be for the “general welfare” of all the people (roads, military, etc.) not for projects benefiting certain individuals, states or groups. A great summary of some of the founders’ refutation of the broad reading of the clause is found here. The General Welfare clause was in no way intended to grant power to the federal government, as the ”Father of the Constitution” explained:
“If Congress can do whatever in their discretion can be done by money, and will promote the General Welfare, the Government is no longer a limited one, possessing enumerated powers, but an indefinite one, subject to particular exceptions.” James Madison, letter to Edmund Pendleton, 1792
Here’s a 72-minute Podcast with a constitutional scholar discussing the general Welfare clause.
More information in a well-written article here