  Using the formalism of constrained superfields, we derive the most general
effective action of a light goldstino coupled to the minimal supersymmetric
standard model (MSSM) and study its phenomenological consequences. The
goldstino-induced couplings become important when the (hidden sector) scale of
spontaneous supersymmetry breaking, $\sqrt f$, is relatively low, of the order
of few TeV. In particular, we compute the Higgs potential and show that the
(tree level) mass of the lightest Higgs scalar can be increased to the LEP
bound for $\sqrt f\sim 2$ TeV to 7 TeV. Moreover, the effective quartic Higgs
coupling is increased due to additional tree-level contributions proportional
to the ratio of visible to hidden sector supersymmetry breaking scales. This
increase can alleviate the amount of fine tuning of the electroweak scale that
exists in the MSSM. Among the new goldstino couplings, beyond those in MSSM,
the most important ones generate an invisible decay of the Higgs boson into a
goldstino and neutralino (if m_h>m_{\chi_1^0}), with a partial decay rate that
can be comparable to the SM channel h^0-> \gamma\gamma. A similar decay of Z
boson is possible if m_Z>m_{\chi_1^0} and brings a lower bound on $\sqrt f$
that must be of about 700 GeV. Additional decay modes of the Higgs or Z bosons
into a pair of light goldstinos, while possible, are suppressed by an extra 1/f
factor and have no significant impact on the model.
