The 29-year-old New Zealander arrives at Ravenhill following three straight defeats with the struggling Dragons.
"The environment at Ulster wasn't great and it was hard to fit in," said Webb.
"They had a really difficult season last year results-wise and they changed coaches three times.
"Once I got a few games under my belt I wanted more. But it was tough. I got sick of training because I train to play, not play to train. In the end, I knew I was excess to requirements."
Webb played just 131 minutes of rugby in three first-team outings for the Irish province including two Heineken Cup appearances after his move from Hawkes Baynin New Zealand last December.
But despite a difficult time on the field, Webb admits he misses the Irish way of life.
"The match at Ravenhill was the first one I looked for on the fixture list because Ulster have the best fans in the Magners League. They are extremely passionate and were excellent to me. It will be great to go back."
The Dragons return to Ireland just six days following a 50-point hammering by Heineken Cup winners Munster, with coach Paul Turner making sweeping changes with six new faces in his side.
Turner said: "The manner in which we leaked points last weekend was disappointing and this has been addressed."
Ulster: C Schifcofske; A Trimble, D Cave, R Dewey, T Nagusa; N O'Connor, l Boss; T Court; R Best (capt), B Botha, R Caldwell, E O'Donoghue, M McCullough, R Diack, K Dawson
Replacements: N Brady, J Fitzpatrick, C Del Fava, T Anderson, C Willis, I Humphreys, B Cunningham
Dragons: P Dollman; G Wyatt, R Sidey, A Smith, R Fussell; J Arlidge, W Evans; A Black, - T Willis (capt), R Thomas, A Jones, L Charteris, J Bearman, G Webb, R Parks
Replacements: S Jones, H Gustafson, A Brown, J Ringer, R Gomer Davies, J Tovey, T Isaacs