Will compressed hydrogen float in air?
Yes. A simple example is an ordinary balloon, which places the gas inside it under pressure (because the tension of the rubber surface adds to the air pressure from outside the balloon), yet the balloon still floats readily.

What you're probably talking about is a theoretical container that can hold highly-compressed hydrogen, like from a supply cylinder, yet has negligible weight. At what point, then, would the hydrogen weigh more than air and the container would settle to the ground?

To answer that, we'll look at the ideal gas law: $PV = nRT$, or equivalently, $P = \dfrac{nRT}{V}$. For our purposes, we'll ignore the temperature increase of the compressed gas by saying this container, while having negligible weight, also has an efficient cooling system so the temperature delta is negligible.

At STP (273*K, 100kPa), one liter of volume filled with hydrogen gas contains:

$$100 = \dfrac{n(8.3145)(273)}{1}$$
$$100 = 2269.8482n$$
$$n = .0441\text{ mol}$$

With hydrogen having a molar weight of 1.00794 g/mol (and $\ce{H2}$ gas having double that), the density in g/L of hydrogen gas at STP is .08890 g/L.

Borrowing from ashu's answer, since his math and mine are within 1% error, the density of air at STP is 1.225g/L (1 m3 = 1000 L). So, in order to have the same mass of gas in the same volume, and thus the same density, you would need 13.78 times the amount of gas than you'd have in the same volume at STP (pretty much 1.225 mol). Because, given a unit volume, double the gas equals double the pressure, the resulting pressure of a container of negligible mass holding enough compressed hydrogen to not float in air is 1377.953kPa. 

In SAE units, that's actually not much in relative terms; only 199.855 psi (call it 200 so it would actually sink in air and not be neutrally buoyant). That's the water pressure at a depth of about 460 feet (140.72m), which human freedivers have matched using dive sleds.