A statement from the presidency confirmed that the bill, which it said "consolidates various laws relating to marriage", had been signed into law.
The bill, which amended existing legislation, was passed by parliament last month to formalise traditional practice regarding marrying more than one person.
"Marriage is the voluntary union of a man and a woman, whether in a monogamous or polygamous union," the presidential statement added.
The initial bill had given a wife the right to veto the husband's choice, but male members of parliament overcame party divisions to push through a text that dropped this clause.
When the bill was passed last month, female members of parliament stormed out of the session in fury after a heated debate.
The National Council of Churches in Kenya (NCCK), which groups more than 40 churches and Christian organisations from across the east African nation, has also spoken out against the bill.
The national Federation of Women Lawyers (FIDA Kenya) has also said it would mount a legal challenge against the law.
"We know that men are afraid of women's tongues more than anything else," female legislator Soipan Tuya told fellow MPs when the bill was passed.
"But at the end of the day, if you are the man of the house, and you choose to bring on another party — and they may be two or three — I think it behoves you to be man enough to agree that your wife and family should know," she added.
As in many parts of Africa, polygamy is common among traditional communities in Kenya, as well as in the country's Muslim community, which accounts for up to a fifth of the population.
Many have said the legislation merely acknowledges something that is already widespread.
"When you marry an African woman, she must know the second one is on the way, and a third wife… this is Africa," MP Junet Mohammed told the house during debate on the bill.
Women are not allowed to marry more than one man.