Youngs Modulus or Modulus of Elasticity 'E' is a material property specific to that material. 'E' is equal to Stress divided by Strain - Strain is original length divided by deformed length and is dimensionless (m/m). 'E' defines how a material deformes when stressed so it is an important parameter in defining deflection. There is therefore no formula to get from tensile strength to Youngs Modulus - E is specific to a material.
If your component's shape is already defined, you can find the minimum acceptable Young's Modulus using the classic formula (e.g., for an axially loaded component of uniform cross-sectional area):
Delta = (FL)/(EA), where F is the axial force, L is the length of the component, E is your minimum acceptable Young's modulus, and A is the cross-sectional area.
Since you know the maximum allowable deflection, this formula can give you the minimum acceptable Young's Modulus (if you know all the other variables.) Then you can use materials textbooks, or a searchable online resource like MatWeb to find a material that meets your minimum Young's moduls requirements and your minimum tensile strength requirements.
If the loading case is not axial, there are other formulas available to calculate E given a certain deflection. If you're using some FEA software, then you can play around with E in that software to see what the minimum allowable value is.