Optical coherence tomography (OCT) is a versatile imaging technique and has great potential in tissue characterization for breast cancer diagnosis and surgical guidance. In addition to structural difference, cancerous breast tissue is usually stiffer compared to normal adipose breast tissue. However, previous studies on compression optical coherence elastography (OCE) are qualitative rather than quantitative. It is challenging to identify the cancerous status of tissue based on qualitative OCE results obtained from different measurement sessions or from different patients. Therefore, it is critical to develop technique that integrates structural imaging and force sensing, for quantitative elasticity characterization of breast tissue. In this work, we demonstrate a quantitative OCE (qOCE) microsurgery device which simultaneously quantifies force exerted to tissue and measures the resultant tissue deformation. The qOCE system is based on a spectral domain OCT engine operated at 1300 nm and a probe with an integrated Febry-Perot (FP) interferometric cavity at its distal end. The FP cavity is formed by the cleaved end of the lead-in fiber and the end surface of a GRIN lens which allows light to incident into tissue for structural imaging. The force exerted to tissue is quantified by the change of FP cavity length which is interrogated by a fiber-optic common-paths phase resolved OCT system with sub-nanometer sensitivity. Simultaneously, image of the tissue structure is acquired from photons returned from tissue through the GRIN lens. Tissue deformation is obtained through Doppler analysis. Tissue elasticity can be quantified by comparing the force exerted and tissue deformation.