It reaches the cerebellum partly through the brachium conjunctivum (superior cerebellar peduncle) and partly through the restiform body (inferior cerebellar peduncle). Pathway for dorsal and spinocuneocerebellar tracts
The sensory neurons synapse in an area known as Clarkes nucleus or "Clarkes column". This is a column of relay neuron cell bodies within the medial gray matter within the spinal cord in layer VII (just beneath the dorsal horn), specifically between T1-L3. These neurons then send axons up the spinal cord, and project ipsilaterally to medial zones of the cerebellum through the inferior cerebellar peduncle. Below L3, relevant neurons pass into the fasciculus gracilis (usually associated with the dorsal column-medial lemniscal system) until L3 where they synapse with Clarkes nucleus (leading to considerable caudal enlargement). The neurons in the accessory cuneate nucleus have axons leading to the ipsilateral cerebellum via the inferior cerebellar peduncle. Pathway for ventral and rostral spinocerebellar tracts
Some neurons of the ventral spinocerebellar tract instead form synapses with neurons in layer VII of L4-S3. Most of these fibers cross over to the contralateral lateral funiculus via the anterior white commissure and through the superior cerebellar peduncle. The fibers then often cross over again within the cerebellum to end on the ipsilateral side. For this reason the tract is sometimes termed the "double-crosser." The Rostral Tract synapses at the dorsal horn lamina (intermediate gray zone) of the spinal cord and ascends ipsilaterally to the cerebellum through the inferior cerebellar peduncle

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References
Further reading
OSCARSSON, O.; UDDENBERG, N. (1 May 1965).
These central processes travel through the dorsal horn where they synapse with second order neurons of Clarkes nucleus. Axon fibers from Clarkes Nucleus convey this proprioceptive information in the spinal cord in the peripheral region of the funiculus posterior ipsilaterally. The fibers continue to course through the medulla oblongata of the brainstem, at which point they pass through the inferior cerebellar peduncle and into the cerebellum, where unconscious proprioceptive information is processed. This tract involves two neurons and ends up on the same side of the body. The terms Flechsigs fasciculus and Flechsigs tract are named after German neuroanatomist, psychiatrist and neuropathologist Paul Flechsig. Ventral spinocerebellar tract
The ventral spinocerebellar tract (or anterior spinocerebellar tract) conveys proprioceptive information from the body to the cerebellum. Historically, it has also been known as Gowers column (or fasciculus or tract),  after Sir William Richard Gowers. It is part of the somatosensory system and runs in parallel with the dorsal spinocerebellar tract. Both these tracts involve two neurons. The ventral spinocerebellar tract will cross to the opposite side of the body first in the spinal cord as part of the anterior white commissure and then cross again to end in the cerebellum (referred to as a "double cross"), as compared to the dorsal spinocerebellar tract, which does not decussate, or cross sides, at all through its path. The ventral tract (under L2/L3) gets its proprioceptive/fine touch/vibration information from a first order neuron, with its cell body in a dorsal ganglion.