There are several international laws and conventions that govern labor unions and worker's rights. The most relevant ones come from the International Labour Organization (ILO) and other international agreements. Relevant laws and conventions are listed below. 

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International Labour Organization (ILO)

The International Labour Organization (ILO) is devoted to promoting social justice and internationally recognized human and labour rights, pursuing its founding mission that social justice is essential to universal and lasting peace.

The only tripartite U.N. agency, since 1919 the ILO brings together governments, employers and workers of 187 Member States, to set labour standards, develop policies and devise programmes promoting decent work for all women and men. 

Relevant Conventions:

ILO Convention No. 87 (Freedom of Association and Protection of the Right to Organise, 1948)

Establishes the right of workers and employers to form and join organizations without government interference.

ILO Convention No. 98 (Right to Organise and Collective Bargaining, 1949)

Ensures unions can engage in collective bargaining without employer interference. 

ILO Convention No. 151 (Labour Relations in Public Service, 1978)

Extends collective bargaining rights to public sector employees.

All ILO Conventions can be found here.

Universal Declaration of Human Rights 

The Universal Declaration of Human Rights (UDHR) is a foundational international document that sets out fundamental human rights and freedoms to be universally protected. It was adopted by the United Nations General Assembly on December 10, 1948, in the aftermath of World War II.

Article 23 protects the right to join and form trade unions. The entire Declaration can be found here.