Reaction force for buoyancy? According to Newton's 3rd law each force (action) has a counter-force (reaction). 
What is the reaction (counter-force) of buoyancy?
 A: We call buoyancy a force, but really, what is it ? It's only gravity. This is only a difference in the gravity force applied to the water and the gravity force applied to your object.
So buoyancy is not a force applied by the water to the object. It's gravity applied differently to the water and the object by the earth. Here, the real force is gravity.
A: I'll attempt to explain the nature of buoyant force with an example. Consider a cube with side $l$ and density $500kg/m^3$, is submerged completely in water. Let the mass of this cube be $m_{cube}=1kg$

We know that density of water, $\rho_{water}=1000kg/m^3$
Now,

*

*Water above the cube exerts a force equivalent to its weight. The cube exerts an equal and opp. force on water above.

$$V_{water}=l^{2}h$$
$$\rho_{water}=1000kg/m^3$$
$$mass_{water}=\rho V=1000l^{2}h$$
$$\therefore F=Weight_{water}=1000l^{2}hg$$
$$~~~~~~~~~~~~~~~~~=9800l^{2}h$$


*Upward force from beneath the cube : Volume of water at $h+l$ (in the figure) exerts a force on water beneath $h+l$. As a result, water below $h+l$ exerts an equal and opposite force on water at $h+l$ and on the cube too, upwards.

$$\text{Upwards force} = \rho ghl^{2}$$
$$~~~~~~~~~~~~~~~=(1000h+1000l)(gl^{2})$$
$$~~~~~~~~~~~~~~~=9800hl^{2}+9800l^{3}$$
Now, by calculating net force on the block, we can obtain the buoyant force.
$$Buoyant force = (9800hl^{2}+9800l^{3})-9800hl^{2}~~~~~~~~~~~~~~~~~~~~~~~~~~$$
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=9800l^{3}=\text{Weight of the fluid(water) displaced.}$$
$$\text{Volume of the cube}=\frac{m}{\rho} = \frac{1}{500} = l^{3} $$
$$\text{Buoyant force on the cube}=9800l^{3}=\frac{9800}{500}=19.6\text{N}$$
CONCLUSION
Therefore, as Pierre said, buoyant force is the result of Gravity only. If you need help in visualising buoyancy, PhET's Buoyancy Simulation can come in handy.
A: The weight of a mass m is m*g, this weight acting in the downward direction will cause a pressure on the fluid below the body. So the fluid must give a reaction force on the body according to Newton's third law. So the reaction force is the buoyant force.
