The woman had been having affairs with both men for more than four years and apparently refused to choose between them.
The agreement sets out a rota for Sylvester Mwendwa and Elijah Kimani to stay in her house and states they will both help raise any children she bears.
Lawyers said their "marriage" would be legally recognised if they could prove polyandry was part of their custom.
Mr Mwendwa and Mr Kimani drafted the agreement after realising they had both been having an affair with the woman in Mombasa County for more than four years, the local Daily Nation newspaper reports.
The laws we have do not talk about it but for such a union to be recognised in Kenya, it has to be either under the statutory law or as customary marriage"
Community policing officer Adhalah Abdulrahman persuaded the two men to marry the woman after he saw them fighting over her, it reports.
"We have agreed that from today we will not threaten or have jealous feelings because of our wife, who says she's not ready to let go of any of us," the agreement says, Kenya's NTV station reports.
"Each one will respect the day set aside for him. We agree to love each other and live peacefully. No-one has forced us to make this agreement," it adds.
Mr Mwenda said her parents had given their blessing, while he is planning to pay the bride price.
The woman, a widow with two children, did not want to be named.
Kenyan family lawyer Judy Thongori told the Daily Nation that the law does not explicitly forbid polyandry - a woman having more than one husband.
"The laws we have do not talk about it but for such a union to be recognised in Kenya, it has to be either under the statutory law or as customary marriage. The question we should ask now is whether these people come from communities that have been practising polyandry," she is quoted as saying.
Polygamous marriages often take place in Kenya, but wife-sharing is unheard of, correspondents say.
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