At a White House bill-signing ceremony on Thursday Bush said that the law allowing the construction of the 1,100km-long fence would make the frontier more secure.
He called the bill "an important step toward immigration reform".
"Unfortunately, the United States has not been in complete control of its borders for decades, and therefore illegal immigration has been on the rise," Bush said.
"We have a responsibility to address these challenges. We have a responsibility to enforce our laws. We have a responsibility to secure our borders. We take this responsibility seriously."
Bush gave the final go-ahead to the bill 12 days before US mid-term elections.
However the $1.2bn funding approved by Bush is much less than the estimated cost of constructing the barrier.
"The decision made by Congress and the US government is deplorable"
The fence's cost has been estimated at up to $6bn and Harry Reid, the senate Democratic opposition leader, said it could cost $8bn.
According to a poll taken by the Opinion Research Corporation for CNN, 53 per cent of Americans oppose the barrier, while 45 per cent support it.
Vicente Fox, the Mexican president, said the fence would not stop millions of Mexicans from heading north in search of jobs.
"It is an embarrassment for the United States," Fox said.
"It is proof, perhaps, that the United States does not see immigration as a subject that corresponds to both countries."
Felipe Calderon, the president-elect who takes over from Fox on December 1, also criticised the US decision.
"The decision made by Congress and the US government is deplorable," Calderon said while on tour in Canada.
"Humanity committed a grave error by constructing the Berlin wall and I am sure that today the United States is committing a grave error in constructing a wall along our northern border."